You need to do a little more archeological digging still. You need to know the whole construction of the floor before you can decide how best to install something new. I'd take up that plywood piece in the kitchen and see what's under it. It's higher than the surrounding floor, so needs to go. You should also be able to see from there what subfloor is under the original kitchen hardwood. It's too bad the space under your entryway is finished, but I'd still do some exploring from below to see what's under there, and to figure out the fix to stop it from squeaking. Is it drywall below or a drop ceiling? I know it probably seems like a pain to tear out drywall, but if you cut out a clean patch, like 2' x the width of the joists, it'll be relatively simple to repair. Just make sure to cut it down the center of the joists so that there's room to screw the patch piece to it later. Cut the hole under the area that squeaks the most, if you can. Have someone walk on and watch the floor from below to see what's moving. It might be as simple as pounding in a couple shims from below, or face-nailing a loose board from above. You want to find out what's underneath the hardwood. It might be laid directly on the floor joists, or there might be 10" wide boards that the hardwood is nailed to. Another thought is to take out a board in the hallway, since that's not original and you want to replace it. See what the subfloor is there. I am a bit puzzled at why, when you've stripped the kitchen down to the original hardwood, it's still higher than the hallway floor. Is your current surface perhaps not the original kitchen hardwood? Peeling back the plywood area will help determine that. BTW, I haven't heard of that stop squeaking product you linked to, so can't offer any personal opinion. And don't pour self-leveling compound over top of hardwood. It needs to go over plywood.

Do not do LVP. It's an ecological and health nightmare. It's a petroleum product, it does not degrade, and it off-gasses some pretty nasty chemicals that are not wise for human consumption. More on that here: https://www.greenbuildingsupply.com/Learning-Center/Flooring-LC/Why-we-dont-sell-luxury-vinyl-tile I have appointed myself a one-woman crusader against this type of product on this forum for which I will surely take some hits. So be it. Have your oak floors sanded and refinished with a protective coating that is on the Greenguard product list.

When I hear someone recount something that makes no sense, I generally figure that someone misspoke or didn't hear correctly. Whenever I see huge variations (3x) in price quotes, I generally figure someone made a mistake. Maybe the third quote will clear things up. Whether wood can be refinished depends on the type of floor and condition. Since you're selling, and already having work done in the house, I'd be inclined to have all the floors redone unless the finisher can match it 90%. If there's any doubt, do it all. This assumes you know what prospective buyers are going to want. I usually recommend the opposite when people are living in the house. Colors and preferences here are all over the place. Usually it seems foolish to upend residents and spend their money when there's a good likelihood the next person won't like their choice, but your situation sounds different since you're already having work done. The only warnings I have about sanding painted floors are that you may find some cosmetic damage and you may end up with paint residual in some cracks.

I recently renovated my 1969 split level house with original red oak floors. On the main floor, I completely refinished and wove in new red oak were there was previously tile and it is all one color now. But, at the landing of the top level, I did not redo the wood floors, picture attached. As you can see they are noticeably different, which I think makes it work. Trying to match and missing is not good. Make it look intentional. I'm not familiar with prefinished hardwoods. Can they be refinished at some point? If so, you'll want to be sure that if you ever do refinish all the floors, they can eventually wind up the same color.