[john70t]

Looks like a big old can 'o worms to me:
-A maximum rise and minimum tread depth is required by code for any commercial/rental use. It's a safety thing. You can get away with it for a personal home but there might be an issue if it's inspected later on, or someone ever falls on them. Insurance would have a stink.

-The stringers have to carry 500lbs++ weight and be locked into the header. Metal might do it. Stairs snapping in the middle is a bad thing. Those look thin. As in 2x4. It's difficult to tell proportions from the fish-eye photos.

-A more gradual stair stringer will extend well into the existing exterior door sweep path. It will intrude into the landing and make it irregular. So an outward-sweep door is needed. Plus you might need a minimum sized landing at the top in front of the door.

-The right side wall to the door looks like it carries the weight of the second floor stairs and the first floor joists....but is floating in air. That load-carrying header might need to get beefed up with a steel beam or glue lams. That looks like a critical vertical load point for the entire structure, to my layman eyes.

-You will probably want a solid handrail to prevent falling all the way down into the basement.

-A different idea (if feasible) Would be to move that door back if possible to allow more stair length and keep the full landing from the outside. The header and section of floor would need a post and much reinforcement. Boxing in a floor cutout would get tricky and need more posts. Who knows what is in there. That could get messy but would keep the pathways usable and safe.