Use a pry bar with a thin putty knife to protect drywall. Cut caulk/paint seams with a utility knife first. Pull nails out from the back to avoid splintering.

Yes, but: Sand down high spots or use construction adhesive for extra hold. Consider backer rod behind moulding to fill uneven gaps before caulking.

Use a miter saw: Set to 45° for standard corners. Coping method: For tight inside corners, cut one piece straight and "cope" the mating piece. Test cuts: Always check fit before nailing.