Quarter round should not be mitred in corners. Use a coping saw to make a circular cut so that one piece one piece will fit over the other. I you're going to paint the quarter round, you can fill in any gaps with quick seal. If you want to varnish, cut carefully.
Sure. A plastic hand miter saw from your nearest hardware store, a coping saw, a hammer, some 1.5" finish nails, wood filler, some caulk (assuming you will be painting), your finger to smooth the caulk, a paint brush, some primer, some paint, your hand to hold the paint brush and most importantly, a 12 pack of your favorite beer!