Do Episode Credits appear in my podcast’s RSS feed?

Yes. Credits appear at the bottom of your episode’s show notes — in the podcast app, just like on the episode page on your site. Any app that displays show notes will show them.

What listeners see is exactly what was locked in when you clicked Apply. The credit is saved as plain text at that point, so there’s nothing to change afterward — no dynamic updates, no re-processing. What you applied is what they get.