Can a person remove tzitzit strings from one tallis katan, and place it unto another tallis katan that one wants to use or likes better?
This is permissible.
see Shulchan Aruch O:C 15:1. The Mishna Brura ibid s”k 3 brings from the Pri Megadim that if other strings are readily available it is proper not to remove the tzitzis, unless one’s intent is to no longer use the original beged as tzitzis [i.e. he plans to remove one of the corners].