1) "I'm going to have to leave here" means that you will be in a necessity to leave the location where you are present. It's the future action of (3).
2) "I gotta have to leave here." is an incorrect sentence. You can however, say "I have to leave here" or "I got to leave here" to mean that you need to leave at the present time.
3) It means that you are required to depart the place.