Determining if this segment is load bearing should be evident to a competent contractor. There are a few things to look for. You have to look above and below the wall in question. In the floor or attic above, you have to determine if there is structure bearing down directly or via headers to this wall segment. Next, you need to look below in the basement level to see if a beam, post or other structure is directly below the wall segment carrying the load to the foundation. While not always true, this wall segment may be load bearing if it is parallel to the longest dimension of the house, usually perpendicular to a gable end and located half way between the two longest exterior walls. There are a few methods of framing that could make this a load bearing wall, even if you have full trusses for roof support, ie; ceiling joists that rest on a center beam directly over the wall in question. As I said, most competent carpenters could look at this and determine it's load bearing status. Obviously, a set of plans would be helpful as well. Even if it is load bearing, a good carpenter will be able to design a header to span the new opening, support the load and allow you to remove the section of wall you want gone.
It can be kind of hard to tell from photos.
Your house plans (blueprints) would tell you for sure, presuming the house was built faithfully to the plans. You really should have a good look at the plans, or get somebody knowledgeable to look at this in person. Or both.
Do you know which direction the joists are running? Floor and ceiling joists will be perpendicular to the load bearing walls (or beams!), not parallel to them. If the joists pass across the top of the wall (or beam) unbroken, then the wall is possibly not load-bearing, depending on your joists, the length of the span after you remove the wall, and the load on the floor above.
If the ends of the joists are resting on the wall or beam, then it is definitely load-bearing.
if there isn't another floor above this one, and you have engineered, prefabricated trusses holding up your roof, this won't be load-bearing. The trusses are engineered to handle the load of the roof by themselves. If they aren't engineered trusses, that doesn't apply.
Is the long common wall of the living room/dining room/kitchen directly on top of (parallel with) the long wall downstairs, and is the opening between the dining and living rooms perpendicular to that long wall downstairs? It looks like the photos might be from different directions? If so, then the common wall with the kitchen is probably the load-bearing wall, and the opening between the living and dining rooms may or may not be, depending on how the joists are laid out.
But you really should look at the plans or get somebody knowledgeable to take a look in person.
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Best Answer
If the structure above this wall (the joists of the second level) is parallel to this wall, then it's highly unlikely that the wall is load bearing -- what load would it bear, if there's no structure present to bring a load onto the wall? The only possibility is that something like a joist lies directly on top of the wall and you haven't been able to discover it yet.
The planned renovation is going to involve quite a lot of drywall repair on the walls and at least a little bit of repair on the ceiling too. You've done all the due diligence that can be done. Now it's time to cut an inspection hole in the ceiling and visually confirm that nothing bears on the top of that wall. I suggest finding the locations of the nearest joist on each side of that wall and cut the hole on whichever side has more wall-to-joist space. You might also choose to cut the inspection hole on whichever side is easier to repair in case the project does not go forward, or whichever side will bother you less if the hole persists for some time until the project work does commence.