I know that if I selected someone in  the Rule 5 draft, that I have to keep him on ML roster for the whole season. But does that include the playoff roster? Can I leave him off that and still keep him? Also, does time on the playoff roster while one's team is in contention count toward ML service time?

The playoff roster is just a subset of your major league roster (which itself is a subset of your 40 man roster).

As long as the R5 player remains on your ML roster, you are good.  This implies that he does NOT need to be on your playoff roster.

Though I believe he loses his R5 status once the regular season has concluded, and can be treated as a "regular" player after that point.

ML service time does not get counted beyond the end of the regular season, so playoff time does not earn service time.

R5 designation drop at the end of the regular season.   You can demote them but you risk demotion penalty.    Remove them from your playoff roster and demote them before ST next season.   Only costs 16k and there's no risk of demotion penalty.

I learned something recently that blew me away. I guess I didn't realize that you can take a AA or AAA player who has never played a ML inning and he can play in the playoffs. Now bear with me because I think we all know that, but I want to explain further.

This particular player won a playoff start and it showed that he was still in AAA. In other words...he was playing in the ML playoffs without ever being officially promoted to the major leagues. WTF? I guess as long as a guy is on the 40 man you can do that. Savvy move on the GM's part. This was one of those AAA phenom pitchers rated close to 80. He got the benefit of promoting him to the majors without ever having to promote him. There are loopholes everywhere.

MikeT, I don't understand. Wouldn't I have to pay the full ML salary if I wait until after rollover to demote him?

Yeah. 343k.   You're paying 327k now.

But if I demote after the season, I would only have to pay a minor league salary next season.

It's up to you what's more important - chance of a demotion penalty or saving $300k.