As defined in the OP, there are two quite distinct questions which I will take in the reverse order.
The Phrase πᾶν τὸ πλήρωμα (= all the fullness), exactly like this, occurs only three times in the NT as noted in the OP (BLB quoted below).
- Eph 3:19 - and to know the love of Christ surpassing knowledge, so that you may be filled unto all the fullness of God.
- Col 1:19 - because all the fullness was pleased to dwell in Him [= Jesus]
- Col 2:9 - For in Him [= Jesus] all the fullness of the Deity dwells bodily.
Thus, Paul uses this phrase πᾶν τὸ πλήρωμα in two distinct ways, both somewhat related:
- Deity exists in all its fullness in Christ
- Jesus followers, who know the love of Christ, have the all the fullness of God
Here we must be careful not to allow more than was intended by Paul. To help go further, let us consider how Paul uses the word πλήρωμα in other places (BLB). In each case the obvious interpretation placed afterward.
- Rom 11:12 - But if their trespass is the riches of the world, and their failure is the riches of the Gentiles, how much more their fullness! [Discussing the full compliment of the Jews?]
- Rom 11:25 - ... A hardening in part has happened to Israel, until the fullness of the Gentiles may come in. [= the full complement?]
- Rom 13:10 - Love does not do evil to its neighbor; therefore love is the fulfillment of the Law. [= love does all that the law demands?]
- Rom 15:29 - Now I know that coming to you, I will come in the fullness of the blessing of Christ. [= with Christ's full bless/approval?]
- 1 Cor 10:26 - for, "The earth is the Lord's, and its fullness." [= everything in the earth?]
- Gal 4:4 - But when the fullness of the time had come, God sent forth His Son, having been born of a woman, having been born under the Law, [= appointed time, or when the time was right?]
- Eph 1:10 - for the administration of the fullness of the times, to bring together all things in Christ--the things in the heavens and the things upon the earth-- [= when the time is right or the appointed time?]
- Eph 1:(22) & 23* - And He put all things under His feet and gave Him to be head over all things to the church, which is His body, the fullness of the One filling all in all. [= this meaning is similar to Eph 3:19 - being filled with God or Christ, presumably, the attitude and love of Christ?]
- Eph 4:13* - until we all may attain to the unity of the faith and of the knowledge of the Son of God, unto a complete man, to the measure of the stature of the fullness of Christ, [= again this is similar to Eph 3:19 and 1:23 - having the love of Christ filling our minds?]
So now, how can these results be summarized? If we exclude the references to the earth, times and the compliment of the Jews, etc, we are left with the following that all discuss the fullness of Christ or God which are marked above with "*". That is, the uses of πλήρωμα in Ephesians appears to be a complete transformation of the character of the believer to be that of Christ to display the attitude of Character of Love to others.
However, this leaves us with those in Col 1:19, 2:9 where the the phrase πᾶν τὸ πλήρωμα is used in conjunction with the verb κατοικέω = to dwell in, settle in, am established in (permanently), inhabit (Strong's). These appear to be making an unambiguous statement about the nature of Christ. Ellicott sums this up in his comments on Col 2:9.
In him dwelleth all the fulness of the Godhead bodily.—Here almost
every word is emphatic. First, “All the fulness of the Godhead”—not a
mere emanation from the Supreme Being. Next, “dwells” and remains for
ever—not descending on Him for a time and leaving Him again. Lastly,
“bodily,” i.e., as incarnate in His humanity. The whole is an
extension and enforcement of Colossians 1:19, “God was pleased that in
Him all the fulness should dwell.” The horror of all that was
material, as having in it the seed of evil, induced denial either of
the reality of our Lord’s body, or of its inseparable connection with
the Godhead in Him. Hence the emphasis here; as also we find (somewhat
later) in St. John, “The Word was made flesh” (John 1:14); “The spirit
which confesseth not that Jesus Christ is come in the flesh . . . is
the spirit of antichrist” (1 John 4:3).
On the meaning of “fullness” (pleroma), see Colossians 1:10; Ephesians
1:3; Ephesians 3:19; Ephesians 4:13. Here it is only necessary to add,
that, as in the later Gnosticism, so probably in its earlier forms,
the word was used for the infinite nature of the Supreme Deity, out of
which all the emanations (afterwards called Æons) received in various
degrees of imperfection, according to their capacity. Probably for
that reason St. Paul uses it so emphatically here. In the same spirit,
St. John declares (John 1:16), “Out of His (Christ’s) fulness have all
we received.” It is not finite, but infinitely perfect; hence we all
can draw from it, yet leave it unimpaired.
Benson reaches a similar conclusion:
Colossians 2:9-10. For in him dwelleth — Inhabiteth, κατοικει,
continually abideth; all the fulness of the Godhead — Believers may be
filled with all the fulness of God, Ephesians 3:19; but in Christ
dwelleth all the fulness of the Godhead, the most full Godhead,
Colossians 1:19; bodily — Really, substantially. The very substance of
God, if one might so speak, dwells in Christ in the most full sense.
“It is plain,” says Dr. Doddridge, “that the Godhead is an anglicism
equivalent to Deity. Compare Acts 17:29. And I cannot think that these
wonderful words are intended merely to signify that God hath lodged in
the hands of Christ a fulness of gifts, to be conferred upon men, as
if the passage were merely parallel to John 1:16-17, as Mr. Pierce
explains it; while Socinus sinks it yet lower, as if it only referred
to his complete knowledge of the divine will. I assuredly believe,
that as it contains an evident allusion to the Shechinah, in which God
dwelt, so it ultimately refers to the adorable mystery of the union of
the divine and human natures in the person of the glorious Emmanuel,
which makes him such an object of our hope and confidence, as the most
exalted creature, with the most glorious endowments, could never of