And when you add sheetrock to an already finished room with trim, you need to remove all the trim.
The window and door will need extension jambs built out for the trim also.
I would remove everything as you will get better results in the end. Sheetrock cuts easily with a score of the paper and a quick snap on the cut.
Take your time, it is easy enough to do.
As for the ceiling , a nice trim board like crown or something fancy looking, will make it look great at the ceiling joint.