I don’t know if there is anything stopping him from acting while he is in office, the only law that I have ever heard of is that they can’t run his films, etc. while he is campaigning, as it gives unequal time to his opponents. They did that with Reagan while he was running for Gov. and Pres, but the day the election, they started airing them again. It is more a personal choice otherwise.
For talk shows, etc. I believe they have to at least offer equal time to all candidates.