ὁ ἦν is not Strictly a Violation of Greek Syntax
You note something that is not exactly correct:
In addition, we find a definite article preceding a finite verb ἦν,
which is a violation of Greek syntax.
Wallace states of what the article "IS" (emphasis added):
At bottom, the article intrinsically has the ability to conceptualize.
Or, as Rosén has put it, the article “has the power of according
nominal status to any expression to which it is appended, and, by this
token, of conveying the status of a concept to whatever ‘thing’ is
denoted by that expression, for the reason that whatever is conceived
by the mind—so it would appear—becomes a concept as a result of one’s
faculty to call it by a name.” In other words, the article is able to
turn just about any part of speech into a noun and, therefore, a
concept. For example, “poor” expresses a quality, but the addition of
an article turns it into an entity, “the poor.” It is this ability to
conceptualize that seems to be the basic force of the article.1
So what we have is an unusual and rare conceptualizing use of the article on a finite verb form, something Wallace notes is possible.2
But why?
Because of the desire to conceptualize an imperfect tense meaning as a substantive, much like the two participles that are found with it, as an appellative. This is because there is no such thing as an imperfect participle in the Greek, the imperfect is only found in the indicative mood.3
The imperfect tense has two primary things significant about it. (1) It indicates an aspect of continuous action, much like the typical present tense. (2) It does so with respect to past time (unlike the present, which is "present" time in the indicative mood).4 As Wallace notes:
The imperfect is often incomplete and focuses on the process of the
action.
With reference to time, the imperfect is almost always past.5
So just as in English there is no such word as "wasing" (a theoretical participle of an imperfect), and therefore no such way to say "one who wasing" as a substantive participle, the Greek likewise is limited. So to convey the idea of "one who was" (carrying with it both the continuous aspect and connection of past time) can probably only be done by doing this odd construction of ὁ ἦν.
So it very much is intentional, but not strictly a violation of syntax, just an unusual use of the language.
Similarly, ἀπὸ τοῦ ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος is not a Violation
Just as the article on ὁ ἦν was acting as a "substantiver" of the finite verb, it is also possible for "the article can turn a phrase into a nominal entity."6 This is what we have here. If it were τοῦ ὄντος instead of τοῦ ὁ ὢν, their would be nothing to carry the prepositional relation through to the other two: ὁ ἦν καὶ ὁ ἐρχόμενος. And if those were each made into some genitive form, one would begin to lose the nominative aspect of what they are doing, as it is the nominative case whose genius is "specific designation" (i.e. "naming"),7 as is being done here.
So the τοῦ is acting as a "substantiver" of the naming phrase ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος, where the τοῦ in the genitive is what is linking that phrase to the proposition ἀπὸ, but the ὁ is still acting with the nominative participles to evoke the appellative qualities.
Your Specific Questions
1. What is the significance of the phrase ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος?
This is translated:
The one who is and the one who was and the one coming.
The significance may be in part as Mark Edward has argued in his answer, that it indicates the name YHWH (though some would argue simply stating Ἐγώ εἰμι does that). However, there seems to be two other points that arise as more significant from this:
First, it appears the reference in Rev 1:8 is to Jesus. He certainly is the topic of Rev 1:5-7. The question is if the v.8 "I" is a self-reference from the perspective of the Father or the Son, especially since the formulation in v.4 would point to being a reference to the Father.8
Evidences that supports 1:8 being the Son speaking are:
(a) Jesus is the chief spokesperson for God, the one revealing what God the Father wants revealed (Rev 1:1). This alone does not resolve the ambiguity, as one can wonder if Christ is quoting God or speaking for Himself in 1:8.
(b) There are no major textual discrepancies in Rev 1:17-18, especially as relates to identification here. I've emphasized key points to the present discussion.
UBS4 - 17 Καὶ ὅτε εἶδον αὐτόν, ἔπεσα πρὸς τοὺς πόδας αὐτοῦ ὡς νεκρός, καὶ ἔθηκεν τὴν δεξιὰν αὐτοῦ ἐπʼ ἐμὲ λέγων, Μὴ φοβοῦ· ἐγώ εἰμι ὁ πρῶτος καὶ ὁ ἔσχατος 18 καὶ ὁ ζῶν, καὶ ἐγενόμην νεκρὸς καὶ ἰδοὺ ζῶν εἰμι εἰς τοὺς αἰῶνας τῶν αἰώνων καὶ ἔχω τὰς κλεῖς τοῦ θανάτου καὶ τοῦ ᾅδου.
TR (Scrivener 1894) - 17 και οτε ειδον αυτον επεσα προς τους ποδας αυτου ως νεκρος και επεθηκεν την δεξιαν αυτου χειρα επ εμε λεγων μοι μη φοβου εγω ειμι ο πρωτος και ο εσχατος 18 και ο ζων και εγενομην νεκρος και ιδου ζων ειμι εις τους αιωνας των αιωνων αμην και εχω τας κλεις του αδου και του θανατου
BYZ2005 - 17 Καὶ ὅτε εἶδον αὐτόν, ἔπεσα πρὸς τοὺς πόδας αὐτοῦ ὡς νεκρός· καὶ ἔθηκεν τὴν δεξιὰν αὐτοῦ ἐπʼ ἐμέ, λέγων, Μὴ φοβοῦ· ἐγώ εἰμι ὁ πρῶτος καὶ ὁ ἔσχατος, 18 καὶ ὁ ζῶν, καὶ ἐγενόμην νεκρός, καὶ ἰδού, ζῶν εἰμὶ εἰς τοὺς αἰῶνας τῶν αἰώνων, ἀμήν· καὶ ἔχω τὰς κλεῖς τοῦ θανάτου καὶ τοῦ ᾍδου.
Clearly, Jesus is the one speaking in vv.17-18. Two things are significant.
One, He calls himself "ὁ πρῶτος καὶ ὁ ἔσχατος" ("the first and the last"). Besides the parallel relation the phrase itself has to the Alpha/Omega phrase (which also communicates first/last idea from the Greek alphabet reference), there is a direct tie between the One Who is the Alpha/Omega and the first/last in Rev 22:13:
ἐγὼ τὸ Ἄλφα καὶ τὸ Ὦ, ὁ πρῶτος καὶ ὁ ἔσχατος, ἡ ἀρχὴ καὶ τὸ τέλος.
Rev 22:13 then establishes an identity connection from these two phrases between the one speaking in 1:17 (clearly Christ) and the one speaking in 1:8.
Two, the statement of v.18 has parallels (not exact) to the statement under discussion in this question:
v.18 | v.8
ὁ ζῶν, | ὁ ὢν
καὶ ἐγενόμην νεκρός, | καὶ ὁ ἦν
ζῶν εἰμὶ εἰς τοὺς αἰῶνας τῶν αἰώνων | καὶ ὁ ἐρχόμενος
Using v.18 for understanding, the first parallel communicates the current being alive. The second parallel speaks of His previous (before death) life. The third speaks of his continued life forever into eternity, which relates simply to the fact that he is alive in order to make a return, a "coming." With Rev 16:5, the parallel is stronger, as the idea of being alive is more direct with the ὁ ὅσιος reference.
Rev 22:13, by including all three forms of reference (i.e. also ἡ ἀρχὴ καὶ τὸ τέλος), ties Christ to Rev 21:6 Alpha/Omega reference as well.
Second, it is just as clear that the phrase is related to God the Father, both Rev 4:8 and 11:17 mention ὁ θεὸς (and the majority reading in the Byzantine manuscripts have it in 1:4 and 1:8 as well; one place where they vary from both the Textus Receptus and UBS texts). In Rev 4:8, it is used of the one sitting on the throne (4:9), which is different from the Lamb, the one who comes to take the scroll from the one sitting on the throne (5:7).
So this phrase ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος (one who is, was, and is coming) is used to create a unique identification, along with the other phrases of Alpha/Omega, first/last, beginning/end, each as identity names for the "oneness" of the Father and the Son who is the express image of God the Father (Heb 1:3).9 So God the Father through the Son is also ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος, just as the Son is also YHWH.
2. Is there a significance in the change from ὁ ὢν καὶ ὁ ἦν καὶ ὁ
ἐρχόμενος to ὁ ἦν καὶ ὁ ὢν καὶ ὁ ἐρχόμενος?
The reversal in Rev 4:8 is more clearly a reference of use with God the Father. The Rev 1:4 also seems so, however, given that Jesus Christ is noted also in the next verse (v.5) as part of the salutation.
If there is any significance, it would seem to be that in this case, it is the declaration of the four living creatures ceaselessly beside the throne chanting this (whereas 1:4 is a reference from John, 1:8 from Christ, and 11:17 from the 24 elders of v.16). So the fact that they put emphasis on the linear order of past, present, future is probably because they have been ceaselessly declaring in from the past, in the present, and into the future (so one is to assume).
The other three references are placing emphasis on the present moment (of John's writing, of Christ's giving the message to John, and of the time for Christ to retake rulership of the earth [so 11:15], respectively).
3. This may relate to the first question, but what is the significance of
yet another violation of Greek syntax in the phrase τοῦ ὁ ὢν («...ἀπὸ
τοῦ ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος...»)?
I answered this above under the discussion of this unusual construction.
4. Finally, is there any similarity in meaning between the aforementioned
four occurrences of ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος and the sole
occurrence of ὁ ὢν καὶ ὁ ἦν καὶ ὁ ὅσιος in Rev. 16:5?
There undoubtedly is some relation, as it is too clear with the ὁ ὢν καὶ ὁ ἦν part (since ὁ ἦν is rare). This phrase, however, in using all "being" verbs, is emphasizing the continuing existence of the righteous one (vv.4-7), a much more direct relation to the idea of YHWH and His name. The focus is not on the "coming" but the in contrast to those being judged in vv.4-7 to their own destruction, the righteous one will forever continue to be.
As a side note, a similar pattern of phrasing is used of the Greek god Zeus by Pausanias (2nd century AD) in his Description of Greece where it is "Ζεὺς ἦν, Ζεὺς ἐστίν, Ζεὺς ἔσσεται." The phrase is noted as "familiar to Hellenic readers ... in the song of doves at Dodona (Ζεὺς ἦν, Ζεὺς ἔστιν, Ζεὺς ἔσσεται) or in the titles of Asclepius and Athene."10 However, the form in the NT is that of the nominative phrasing discussed above (a name designation of both the Father and Christ), as opposed to the assertion here. Also, the NT form, except in Rev 16:5, emphasizes the "one who is coming."
Just for sake of a more complete answer, here is Wallace's statements about 1:4...
8) With Finite Verbs
This usage occurs only in one set phrase found in the Apocalypse alone.
Rev 1:4 χάρις ὑμῖν καὶ εἰρήνη
ἀπὸ ὁ ὢν καὶ ὁ ἦν καὶ ὁ ἐρχόμενος grace to you and peace from the
one who is and the [one who] was and the one who is coming
The syntax here is doubly bizarre: not only does the preposition ἀπό govern a nom. form, but the Seer has turned a finite verb into a
substantive. The imperfect verb is possibly used since no imperfect
participle was available and the Seer did not wish to use the aorist.
If the author of this book is the same as the evangelist who wrote the
Gospel of John, the parallel between the ἦν in the Johannine prologue
and here may be more than coincidental: both would affirm something
about the eternality of the Lord.
Cf. also Rev 1:8; 4:8; 11:17; 16:5.11
NOTES
1 Daniel B. Wallace, Greek Grammar Beyond the Basics - Exegetical Syntax of the New Testament (Zondervan Publishing House and Galaxie Software, 1999), 209.
2 Wallace, 231.
3 William D. Mounce, Basics of Biblical Greek Grammar, 3rd. ed. (Grand Rapids, MI: Zondervan, 2009), 182.
4 Mounce, 183.
5 Wallace, 541.
6 Wallace, 231.
7 Wallace, 37.
8 Theologians are on both sides as to who is speaking in v.8 (note: most of these are from a Protestant perspective; they are listed in no particular order). It is important to note that those ascribing it to God the Father in v.8 still see the phrasing as applicable to Christ from other passages.
On the side that it is God the Father, some examples are: (1) Robert James Utley, Hope in Hard Times - The Final Curtain: Revelation, Vol. 12, Study Guide Commentary Series (Marshall, TX: Bible Lessons International, 2001), 23; (2) Kendell H. Easley, Revelation, Vol. 12. Holman New Testament Commentary (Nashville, TN: Broadman & Holman Publishers, 1998), 14 (under the discussion for v.4); (3) A.T. Robertson, Word Pictures in the New Testament (Nashville, TN: Broadman Press, 1933), Rev 1:8; (4) W. Robertson Nicoll, The Expositor’s Greek Testament: Commentary, Vol. 5 (New York: George H. Doran Company, n.d.), 340; (5) Warren W. Wiersbe, The Bible Exposition Commentary (Wheaton, IL: Victor Books, 1996), 2:569; (6) Robert B. Hughes and J. Carl Laney, Tyndale Concise Bible Commentary (The Tyndale Reference Library. Wheaton, IL: Tyndale House Publishers, 2001), 735; (7) D. A. Carson, R. T. France, J. A. Motyer, and G. J. Wenham, eds., New Bible Commentary: 21st Century Edition, 4th ed. (Leicester, England; Downers Grove, IL: Inter-Varsity Press, 1994), 1426; (8) Roy B. Zuck, A Biblical Theology of the New Testament (Electronic ed. Chicago: Moody Press, 1994), 182; (9) Rolland McCune, A Systematic Theology of Biblical Christianity: The Doctrines of Man, Sin, Christ, and the Holy Spirit Vol. 2 (Allen Park, MI: Detroit Baptist Theological Seminary, 2009), 98.
On the side that it is God the Son, some examples are: (1) John F. Walvoord and Roy B. Zuck, Dallas Theological Seminary, The Bible Knowledge Commentary: An Exposition of the Scriptures (Wheaton, IL: Victor Books, 1985), 2:929; (2) Robert Jamieson, A. R. Fausset, and David Brown, Commentary Critical and Explanatory on the Whole Bible (Oak Harbor, WA: Logos Research Systems, Inc., 1997), Rev 1:8; (3) Marvin Richardson Vincent, Word Studies in the New Testament (New York: Charles Scribner’s Sons, 1887), 2:414; (4) Kenneth S. Wuest, Wuest’s Word Studies from the Greek New Testament: For the English Reader (Grand Rapids: Eerdmans, 1997), mentioned in "Bypaths in the Greek New Testament" under discussion of 1 Pet 2:21; (5) Lewis Sperry Chafer, Systematic Theology (Grand Rapids, MI: Kregel Publications, 1993), 1:333; (6) William Greenough Thayer Shedd, Dogmatic Theology, edited by Alan W. Gomes, 3rd ed. (Phillipsburg, NJ: P & R Pub., 2003), 261; (7) Louis Berkhof, Systematic Theology (Grand Rapids, MI: Wm. B. Eerdmans publishing co., 1938), 94; (8) William Burt Pope, A Compendium of Christian Theology: Being Analytical Outlines of a Course of Theological Study, Biblical, Dogmatic, Historical, Volumes 1-3 (London: Beveridge and Co., 1879), 2:254; (9) Charles Caldwell Ryrie, A Survey of Bible Doctrine (Chicago: Moody Press, 1972), n.p. in elec. ed. (see ch. 3, under "The Deity of Christ").
9 I hold to a hermeneutic that sees unity in the Scripture, and so a reference from Hebrews is perfectly valid as a proof point for discussion in Revelation.
10 Nicoll, The Expositor’s Greek Testament: Commentary, Vol. 5, Rev. 1:4.
11 Wallace, 237.