I am confused about what are the joist and not the joists in my basement. It is a 100 year old house. I have one main bean that runs front to back (supported by columns- the kind with a large cement bottom you might see when building a deck, the term is escaping me at this moment- in basement) and then other ones that run perpendicular (side to side) to that main beam. Are the load bearing walls most likely the ones that also run perpendicular to the large main beam or the ones that run perpendicular to the smaller side to side beams?
I have a wall in the kitchen that runs side to side (perpendicular to that main beam, but with the smaller beams) that we would like to remove a section of. When I look in the basement there is one column under that wall (but also under the main beam and next to a fire place that is being removed) and then a small metal floor jack where there is a vent going up to the second story. There are also other random floor jacks around.
My neighbor is a self employed carpenter and has offered to come look, but I thought I should ask here as well. More opinions=more certainty

If the wall is supported by a support that looks asthough it was built with the house, then chaces are it could be load bearing. However that's only half of the equation. You also have to look at what's above the house, what type of roof you have, upstairs rooms etc. If there is a wall right above the wall you are talking about on a second floor, then the wall in your kitchen is probobly load bearing.

To find if a wall is load bearing, you have to study what's above and below the floor.

As far as the floor jacks, these were probobly installed by do it yourselfers who were wanting to level out a sagging floor. However I have seen them used (in my house for instace) to support new load bearing walls.

For instance, someone somewhere along the years finished my attic and turned it into a room, the added weight on the second floor probobly pushed down on a part of the ground floor that was not properlly supported for the attitional load. So whoever installed three floor jacks right under the wall system in the basement.

Legal? Probobly not. As any support that is load bearing in a basement should be supported by a proper footer. These are just floor jacks sitting on a concrete floor, which is probobly 3" thick, with a small gap underneight. Over the years, the weight of the attic and my other sagging floors has formed cracks in my basement floor. Not severe, but will probobly need to be addressed in the next 30 years.

Food for thought.