1. While removing the door, a couple of tiles broke out with the sheet rock. When purchasing sheet rock for this purpose, what should I ask for? I am assuming I will need to replace all of the sheetrock under this area. Is it possible to buy just the amount of sheetrock needed or am I going to have a lot of left over sheetrock? (The tiles I am removing are 4 in. square and are about 4 feet up the wall)
First of all how much sheetrock did you break off? Did you just tear the paper or is it an actual hole, which is what I'm guess since those tiles (esp being there so long) will really tear up the sheetrock when you try to remove them, thus making it really difficult to "patch" just a row.
Anyways, for bathroom (or anywhere that's a wet location) you need to get what is called green board. Green board is specially made to be water resistant. Any of the BORGs should carry it, and it will come in 4x8 sheets, but the cost should be 10.00 or less.
2. I want to remove the caulk from in between the tiles. Is there something that I can use to remove it easily without messing up the tiles.
Not much special here except elbow grease. I would start by using a sharp razor blade to cut the caulk (being careful not to scratch the tub by going too deep) and begin removing with fingers. Again, the BORGs should carry a small plastic tool that has a hook on it to remove caulk that you could try also.