I think you are going to find a wide variety of answers to your questions. It's really something that comes down to philosophy and needs of the team.
When I was head coach my better positions players were usually my pitchers so they had to hit, pitch and field. If they pitched on a Monday, with a heavy workload, and we had a game on Tuesday the pitcher from Monday would either just DH or try to hide them at a position that probably wouldn't require much throwing. But there would be the occasional player who could pitch on Monday and play SS on Tuesday and I think some of that can be attributed to how in shape they were based on how much they throw and run.
I would try to get them courtesy runners when they were on base but my more athletic pitchers would have the choice and most of the time they chose to run.
I had a few guys who were just pitchers only but that was because they were terrible hitters or terrible fielders.
So overall I let the needs of my team and skill of my pitchers determine how I used them.