Load bearing wall or not?
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?