this is supposed to be a tzeentch list, the hq should not have a different mark.I would go with sorcerer with lash of submission. You can have this on a prince but he can't hide in a unit. V. useful spell.
see above.Daemon Princes cannot join a squad so i wouldnt give him a lot of stuff. Usually i just give him wings and a mark of nurgle with nurgles rot. Sometimes he has wings and mark of khorne. Its up to you but if you want psychic abilities then give them to your sorcerer