Egress from basement bedroom?

[lmnop123]

We are looking to purchase a house in New York state with a partially finished basement. The family room in the basement has been finished to code with a egress window. There are full size doors to two unfinished areas. One of these, an unfinished laundry room area leads to another room that we would like to turn into a bedroom and add square footage to the house by cutting another egress window/well.

The question I have is regarding the door from the bedroom. Currently, it is a full size door that leads into an unfinished laundry area with some low pipes and ducts, etc. The door from the laundry room into the finished family room is a full size door, but has some ductwork that is a few inches lower than the frame on the unfinished side. We would prefer to have a door cut directly from the bedroom into the finished family room, but the only convenient location for that is in an area with low ceiling due to pipes and HVAC stuff. The ceiling here is only ~6'4".

So, my questions are:

1. Will a 6'4" door be sufficient to call this a bedroom?
2. If not, will the door through the unfinished laundry room be sufficient? If not, is the issue that it is entering an unfinished area, or is it that there are some things blocking the top few inches of the door?
3. I think our last option may be to go in through the other unfinished area, but there are also some low pipes in that area, so I am not confident of that option either.

[Jerry Peck - Codeman]