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.

I have not heard of that brand but we purchased the Bella Cera Ruscello flooring and when the boxes showed up it said the dreaded "Made in China" on them. What could I do at that point? We had it installed and are very happy. There is not one piece in the 1100 sq ft that has a flaw. Now, it has only been a few months, but no problems so far... And we also did about 60 sq ft of LM St Laurent flooring in our vanity area almost 2 years ago, it was "Made in China", which I did not know until later, no problems with it either.

Laying the new floor in the same direction as the old floor is not the normal way to go about this. In the building industry, it is more common to see layers that are staggered or "bricked". In other words if layer #1 is laid in a North-South direction, then layer #2 (the top layer) is laid perpendicular to it in an East-West presentation. If you want to run the new flooring in the same direction as the old, you will want to use some underlayment (plywood) over top of the old floor so that you can maintain the "staggered" or "bricked" layering system. That is one way to maintain the North-South presentation. Please work with hardwood flooring professionals who have some experience renovating these old gems. They will have seen what worked....and what didn't. Their experience will be invaluable on a project like yours.

I'm going to dissent on whether this is subfloor. Subfloor boards here are generally laid on the diagonal. If they weren't, I would think the end joints would each fall on a joist. That means joints would line up across the room at regular intervals (often 16" apart). I can see joints in the bedroom picture that don't line up. As long as there's enough wood above the tongue and groove these floor should be able to be refinished. I'd caution against filling the cracks. Quite often they're the result of seasonal changes, but more likely were caused by a catastrophic event (or events). This means the floor is likely to be loose. Loose floors will move when walked on and the filler will work it's way out. If you walk on the floor with bare feet (and are weighty enough) and can't feel movement, you can risk having them filled during the sanding process. If the floor does move, the filler usually comes out of the traffic areas first making them look bad compared to adjacent areas where the filler is intact.