The Greek translated "for this reason" is διὰ τοῦτο (lit. "because of this"). The phrase is formulaic and uses the neuter demonstrative pronoun τοῦτο ("this") regardless of the antecedent, which is generally abstract. So to OP's #1: there is no strictly syntactic explanation apart from the context. Starting in v. 21 Jesus says:
ἓν ἔργον ἐποίησα καὶ πάντες θαυμάζετε
I did one work and you all marvel
Given the characterization in v. 23 (see below), "one work" here must refer to the healing of the man by the pool Bethesda (5:1-11) that elicited discussion about his attitude toward the Sabbath (vv. 12-18).
διὰ τοῦτο Μωϋσῆς δέδωκεν ὑμῖν τὴν περιτομήν...
διὰ τοῦτο Moses gave you circumcision...
καὶ ἐν σαββάτῳ περιτέμνετε ἄνθρωπον.
and on the sabbath you circumcise a man
εἰ περιτομὴν λαμβάνει ἄνθρωπος ἐν σαββάτῳ
if a man receives circumcision on the sabbath
ἵνα μὴ λυθῇ ὁ νόμος Μωϋσέως
so that the law of Moses may not be broken
ἐμοὶ χολᾶτε ὅτι ὅλον ἄνθρωπον ὑγιῆ ἐποίησα ἐν σαββάτῳ;
are you angry with me for making a whole man healthy on the sabbath?
Although it has been suggested that διὰ τοῦτο belongs with the preceding verse (i.e. "you marvel because of this"), in Johannine usage (and in fact in normal Koine), the phrase always introduces the content for which it provides an explanation. This was pointed out by Abbott (Johannine Grammar, 1906) and is picked up by most modern commentators. The phrase points to what precedes as an explanation for what follows: "on account of this [that I have just mentioned]..." (Carson). I have found two distinct but related explanations offered on the nature of causality:
"This" refers to Jesus's "work" by Pool of Bethesda: Moses enjoined circumcision, which was to be performed on the eighth day regardless of the Sabbath, as a precedent for Sabbath activities such as the healing. The principle of qal waḥomer can be seen here: if circumcision, involving only part of the body, is to be performed on the sabbath, how much more so Jesus' more comprehensive healing of "the whole body" (v. 23; cf. Matt. 12:11-12).
"This" refers to the larger implications of Jesus' "signs" in John's Gospel: Moses prescribed circumcision to foreshadow and prepare the people for the more thorough cleansing effected by Jesus, the perfecting of "the whole man" hinted at in v. 23. As Hoskyns put it, circumcision was given,
"that it should be a type and anticipation of that greater and entire healing by the Christ, which also of necessity displaces the sabbath."
1. Leon Morris, The Gospel of John, NICNT (Eerdmans, 1995), 361-362.
2. D. A. Carson, The Gospel According to John, PNTC (Eerdmans, 1991), 314-315.
3. Hoskyns, E. C. The Fourth Gospel. ed F. N. Davey. London: Faber & Faber, 1947. Quoted here from George R. Beasley-Murray, John, WBC (Zondervan, 1999), 109.