1. Everything should come out of the room, but there are exceptions. I am doing a bathroom where the built in cabinet was installed before the floor, including the mud base. The customer decided to leave that in place, which I agreed. But definitely remove toilet and do under that. You may have to change the toilet flange. It should level to 1/4" above finished floor.
2. I do floor first, wall overlaps floor to reduce water migration problems.
3. Start your layout down the middle, not necessarily the actual installation. Tiles should be balanced so the same amount of tiles is on both sides. But that often leaves a very small piece of tile at the edges. If that is the case, I start the tiles from the most visible points with full tiles, and leave cuts in low visibility areas.
4. Start at the bottom and work your way up, use spacers to keep grout joints correct as you go. If using small butt edge tile, no spacers needed.
5. Not sure what you mean, but tile up to the tub leaving about 1/8" for caulk. There are caulks to match grout color.