Walls – Is the closet wall load bearing

In general, load bearing walls are placed above and parallel to (with as little offset as possible) the beams below them.

I would span another beam or mini beam parallel to the first one, to support the joists mid span. I would start out with screw jacks (raising a new beam) and some form of force plate over your slab (steel over plywood to support and distribute the bottom of the jacks), and S l o w l y elevate. 2 inches is a lot of movement. This elevation process should be done over months. You may find that stabilization is all that is necessary, (or prudent). If you add 1/2 to 3/4 at your lowest point, you might be happy.

Monitor what is happening at the original beam. You may find a gap developing there.. If that is the case, you may have to raise the original beam slightly or shim the beam to joist connection with tapered shims.

Once you're happy with the final leveling, permanent columns (and footings below them) are the proper conclusion.

Yes, the new plan really helps. Let’s call North going up. So, I see the basement bearing walls/beams run East-West and is on the South side of the stairs.

So, 2x10 joists at 16” on center will support say live load (people and furniture) of 40 lbs. per square foot plus a dead load (framing, ducts, etc.) of 10 - 14 lbs. per square foot, depending on the species and grade of lumber. This is perfect for current Code compliance.

However, the joists in the 2nd floor sitting room appears to span much further than that if you remove the wall between the kitchen and dining room.

The risk to removing this wall is that the floor will sag and crack the ceiling in the kitchen and dining room...or worse, the 2x10’s are spliced over this wall and they will fail.

So, you’ll need to do a little more investigation. On the 2nd floor, what is the distance from the South wall of the stair to the South exterior wall?