We have pretty much the exact same color trim as you - sort of an aged Chestnut stain color. If your floors are white oak, I would not stain them - leave the wood au natural (our white oak floors are natural). If you want a finish that will get more golden with age, I'd go with a clear oil based finish. If you do that, be warned, you'll have to move out for a few days after the finish is applied - it really stinks. Shellac is a great finish and it can be touched up easily, but it won't be as durable as oil. I don't like varnish finishes - to me they don't look 'historic'.

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.

It looks to me like your walnut furniture isn't "too dark" for dark stained floors. It sounds like you enjoyed having the high-contrast look of the maple floors and the walnut furniture (it sounds lovely). I would suggest you going for the darker stain. Darker than your furniture. This way the beautiful graining of the walnut furniture will pop. Red oak, naturally has a busy grain pattern, and it also has a lot of variation in color when kept natural. I think it may look like you have too much going on if you keep the Oak natural. I also understand that you may prefer the water-based finish, but as a professional, I have to say that especially on the steps and in the entryway, it's not going to last nearly as long as an oil-based finish. So again, if you choose a dark stain color, you can have a win-win situation. The finish can then be oil based, giving you many more years of protection, and you can bring back the beauty of the high-contrast style in the new home. Dark floors, medium furniture, light walls and super white trim = stunning. Plus, with your beautiful big and open entryway, the dark stairs and floors will look really amazing with the light walls and trim. The Flooring Blog The Couture Floor Company

Matching a stain color means a lot of testing. The same color in a different batch on a different wood can be different. What kind of finish was applied. An oil based finish creates an amber color, where water based finishes do not---making a huge difference. If trying to match an oil based finish color with a water based finish, you will need a toner added to the finish. Hopefully, you will have several scrap pieces on which to experiment. Both with stains, toners, and finishes.