When gutting a room, do I need to remove the trim and sill around the window ? I have replacement windows that have caulk around the inside trim

What do you mean by gutting a room? If you're not removing drywall around the window then you should be able to leave it alone.

Usually not the sill but yes to the trim and the trim under the sill.

Buffet, you really would need to be a bit more specifi about what you are doing. The trim is on top of the drywall but the sill is part of the frame.