Yes, it is probably load-bearing due to the stair opening; if the staircase had gone 90 degrees in either direction, that wall section would not have been load-bearing. You have either one or two beams resting on the wall section; if you locate the beams, you'll know where you can place pillars instead of the wall.
What does this really mean? If I take down the interior ceiling, I will see the beam. ?
Can I then place a column there and then tear down the wall?
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Or is it enough to keep a little of the wall where the beam rests against?
What does this really mean? If I take down the ceiling, will I see the beam?
Can I then place a column there and then tear down the wall?
Or is it enough that I retain a bit of the wall where the beam is supported?
Maybe dumb questions I'm completely new.
I can't answer that. You have openings on both sides of this wall. Here, one would probably need to calculate the deflection of the floor structure when the wall is replaced with a column.
Is it only the part of the wall above the stairs you were thinking of removing? Otherwise, it looks like the wall supports the stairs. Probably also the floor on the upper floor. It might be a good idea to remove a bit of the ceiling and see how the floor meets the wall. If it's an old wooden floor on wooden beams, you might easily see in which direction the floor spans. If the wall is load-bearing, it might be a good idea to replace the wall with a beam supported by two pillars/alternatively extended to adjacent walls. A local structural engineer could probably determine what works best in your situation.