A. This is the original (unmodified, as the Americans deleted this phrase) WCF.
B. In my opinion, the inclusion of this line had more to do with politics of the day than theology. Henry VIII had justified his desire for annulment (diligently sought for a long time before he broke with Rome) by an appeal to the "illegitimacy" of his marriage to Catherine of Aragon on the basis that she was previously married to his brother, the former king.
Questions-Answers:
1. Properly read and interpreted, OT laws concerning sexual immorality, including laws that regulated degrees of consanguinity, are valid in NT times, according to the Jerusalem Council, Act.15:29. If the Gentiles, whose sexual mores were utterly corrupted, were to have clear guidance as to what constituted purity in God's sight, and what behaviors were to be put away, they had recourse to the standards God had formerly inscripturated. New Covenant morality was unchanged in this respect. Gentiles did not need the NT to spell out every improper relationship (though, it clearly opposes a number of them explicitly). Bestiality is not once mentioned in the NT, but it is definitely condemned as sexual immorality in the Mosaic law.
So, it is not the case that we go to the OT laws, and pick/choose what we like or don't. We exegete the judicials and ceremonials for their moral content. And we sometimes find laws (after the Decalogue) that are almost purely moral in nature. And the laws of sexual-conduct are mostly of this sort.
2. Lev.18:16 prohibits wife-sharing/swapping. John the Baptist used it to condemn Herod, Mt.14:4. Lev.20:21 seems to complicate the matter, since the section it is in (incl.vv19-20) appears to address forbidden close-marriages which have no living husband-figure. But both vv20-21 deny valid marriages to Israelites beyond blood-connection degrees, extending those limits to former spouses of near kin. In seeking to interpret the laws properly, note first the penalties declared fall short of a death sentence--one indication that these restrictions went beyond the law of nature's, and were a positive limit from God for his separated nation. The union was one that cost the participants significantly in social acceptance (bearing their sin).
The key of understanding is the laws of inheritance, and the maintenance of individual tribal and even family identity (the nation was not to assimilate to another, nor were the tribes to homogenize). The land itself was to be passed down within particular families. So limits were placed on the confusion that could be created by cross-connected family ties. Dt.25 plays into this. It covers the law of levirate marriage, which was a law related to inheritance and to social provision for widows (no Social Security in those days). It belonged to the realm of the kinsman-redeemer/avenger duties.
Here is the key factor: the fruit of this union--first a positive prohibition, in another special case reversed into a command--was not to "count" as the son of the actual father, but of the dead brother. So, "childlessness" was still a factor in the levirate marriage. This causes us to recognize that "childlessness" of Lev.20:21 means "legal-childlessness." Children of such unions were regarded socially as landless (at best), disinherited, perhaps worse. "Childless" doesn't mean the couple would be stoned before they could have children, or that (necessarily) supernaturally they would be held back from having children. But their disregard for the Law would have intergenerational consequences. All that, unless the marriage were properly contracted as a socially acceptable levirate marriage (as Boaz did for Ruth), in which their child would be publicly praised and blessed.
So, in the end we should be able to see that here is actually a case where in Israel, for the cause of Messiah's future birth and the preservation of the holy nation, there was careful regulation of what was not a "natural" prohibition, but was in fact ceremonial/separational. And for this reason, it is dispensable. This limit was not intended to regulate all peoples and times. Henry VIII was wrong to seek an escape from his honest marriage (and too anxious for an heir); though his break with Rome surely was providentially used of God to further the Reformation in England.
3. Philip was alive, Josephus tells us. Even a divorce (which there wasn't) would not have made this incest OK. Herod was Edomite, though he ruled the Jews and judged the holy land. Lev.18:16 more naturally condemns him in general.
4. 1Cor.5:1 demonstrates terrible confusion. The father is almost certainly alive. If not, it is more difficult to see how even the pagans (of that debauched city in particular) could have been scandalized by the details of the liaison. And yet, if she was legally his mother, that might easily give even a Greek (think Oedipus) pause. Bottom line: a son does not sleep with someone his father slept with; that should be abominable in any society, a clear case of incest/confusion. (cf. Amos 2:7)