1) Topical antiseptics, including listerine, have not been studied for their effectiveness in STD prevention
. The best guess, based on distant past experience with other antiseptics (from thw WW II era) suggests little effect. Washing after sex can't hurt, but I doubt using listerine, alcohol, etc does not any difference beyond the minor benefit of soap and water.
2) There are no data on the per-exposure risks from oral sex for any STD other than HIV.