Which way do the stairs come down?

they come down on the opposite side of the ducting. where it says 56.5

So, I spent the last 15 minutes on a drawing program trying to figure this one out, and there are a lot of complicated restrictions that this drawing can't answer. I think you should talk to either a local architect who can come look at what you have and find the answers to a lot of questions onsite or reconsider your restrictions. One bedroom and a bathroom using the existing plumbing is very doable. But if you need egress windows for 3 rooms on a 29' wall, you have less than 10' of space per room. Even knocking that down to 2 bedrooms and a hall with the stair width currently in place and the toilet and sink drains in the floor where they are is extremely complicated. You have a lot of wasted space in the back of the basement under the header if you just line the rooms up against that wall.

I'm sure there's a creative way to answer most of your brief in this space, but I'm not sure it can be answered on an online forum. I think your best option and the one that would save the most time and money would be to have a few people come in and bid the work and provide you with their solutions. Otherwise you're restraining whoever you hire to do this work by quite a lot. And no - unless you are a contractor, I don't recommend trying to work out this plumbing and egress issue on your own.

Good luck, and sorry I couldn't offer a magic wand solution!