Hi hope all is well. I’m trying to build a doorway in a masonry passageway in basement. I want the door to swing into the room but have several problems. (Picture attached)

1. I have about 77in in height under hvac main truck. If I frame for prehung door not sure what my rough framing should be to get as much height as possible.

2. The beam above sits in between passageway making it difficult to attach to ceiling if I want door near entry way. Can I attach tapcon side 2×4 into mason wall with a top plate nailed to that without it being attached to ceiling?

3. is there a better solution then a swinging door should I be looking at a sliding door?