re: Staircase structural support question

I'd be going the other way, you need to figure out how you're going to get the toilet and sink drains connected to your existing plumbing before you figure out the stairs. Your house isn't going to fall down if oyu remove that framing. You can do the stairs 50 different ways, but for plumbing, gravity only goes one direction.

This isn't as simple a job as i think you're picturing. You're not putting a 6" hole in your slab, you're busting out a 6" trench through whatever adjacent rooms are there to get to the nearest properly sized under slab sewer pipe.

For the landing, I came up with the lowest profile plan: get a 1/2" steel plate the size of the landing, weld 6" flat bar up from the steel plate on the two sides the steps aren't (picture a pan with only two sizes, lag bolt to existing framing. You can actually put it on 3 sides and bolt it to the landing on the left as well. Boom, zero profile landing. You'll have to add some strapping from the pan to the top plate above to hang the steel plate better than on just the studs above where your door is going.