Don

Yes, one needs to strive to obey all commandments of all covenants one is in.  Do not enter a covenant (e.g., marriage) if you do not intend to keep your vows, for example.

You cannot divide a covenant up, the Bible says it cannot be done, if in the Mosaic covenant, keep all those commandments that apply to you and that you can do.  Many Messianic Jews try to do this, they keep Sabbath and kosher and I do not see this as wrong, they are honoring God by what they do.

There is some 1st century context that is useful to understand some of the NT.  Most gentiles were pagan but some were called God fearers and were allowed in the temple up to the court of the gentiles.  In effect they were on the road to becoming a Jewish convert and stopped part way.  This was allowed, they could go to synagogue and learn, see Acts 15:21.

Mikveh baths were a part of 2nd temple Judaism.  This is where the idea of baptism of believers came from.  The Jews would do this to be ritually pure to enter temple areas.  It was also the very last step of conversion of a gentile, when they came up out of the mikveh bath they were considered Jewish with all rights and responsibilities.  Before that they needed instruction, to be circumcised if male and to pay for a temple sacrifice, this last was changed to a contribution after the temple was destroyed.

Being baptised is one of the early acts of obedience of a believer and is a public declaration of the inner transformation.  This is also where Jews are freed from the being in the Mosaic covenant by dieing in baptism (Rom 6:4, Col 2:12) to enter the new covenant see Rom 7:1-6, which is a better covenant, e.g.,  God commandments are written on one’s heart and not just stone or paper.

Yes, faith and trust are implied in the Hebrew and Greek, it is English that makes them seem different, but it is good to point out what it means Biblically.

On sexual immorality, see 1 Cor 5:1.  There was a concept among pagans about sexual immorality, but it was not the same as the Jewish concept.  The Jews are asking to meet the commandments of the Jewish understanding.  Recall that some gentiles might be new believers.  Paul teaches not to be immoral also.