1. The "new" bolts are only meant to hold on those caps
2. You need to transfer the stud
3. You need to read the instructions, but typically the compressor does not come with oil in it, just assembly oil.
4. Remember there are several different types of PAG oil
5. General rule of thumb is to drain the old compressor, if you get more than 1 ounce out, add in what came out into the new one. If you get less than 1 ounce, add 1 ounce. Typically you would look on a service program to find out a factory specified amount when changing any A/C component.
Stud extraction.....
1 way is to PB blast it, put 2 nuts on it if possible and turn the lower nut to loosen. It will press against the top one and lock them together.
I would avoid using vise grips, it usually tears up the threads
Worse case, you need to go to the hardware store and get new studs, OR get a long enough bolt and use a bolt instead of a stud.
Hope that helps a little.