Will gently hammering thumbtacks into my wall help them stay better?
The thumb tacks will hold best if they go straight in to the wall without wiggling. If they move back and forth as they're going in, they'll create a larger hole from which they could more easily be pulled. If you can push the tacks all the way in without side to side movement without using a hammer, then there's no advantage to using one. If the hammer allows you to push them in more easily, push them in straighter, or if you can't push them in all the way without a hammer, then the hammer would be better.