1: MLB is testing this in AA and AAA. 99% of the time, the clock starts immediately. As Max said, if a batter gets thrown up and in, we can hold the clock. But on a batter time out, the clock starts immediately.
2: A coach or manager has until 20 seconds to get a fresh 30 seconds on a player initiated trip. If they come out after 20, they can either use another visit to get a reset or be walking off the mound before 0. This is also a AA and AAA experimental rule.
3: You would wave in the new sub and point to wherever the new player is playing. Unless it’s unannounced, which then the press box probably saw it anyway and will announce it