1. Little bit of WD-40 on a rag, and a little rubbing, or some Goo-B-Gone.
2. Yes. Light sanding is always good, even if it's not painted. Also, it's a good idea to do a light solvent wipe before you paint as well, to get those spots the paper can't reach.
3. Yes, it IS possible to do this with a Dremel only, but it will be rather difficult. I hope you have a lot of cutting disks, and some patience. The best way to do it, IMO, is to trace the outline of your window, and cut JUST INSIDE that line with your dremel, and then hand finish the rest with files and sand paper.