I have 4 areas in my current house that were done at different times. Each floor was laid based on the direction that worked for that room. In the doorways, we used a piece of the hardwood and added an extra tongue or an extra groove depending on the need. It's all the same thickness, so there's no "speed bump", but in the doorway of every room, there's a piece that was placed specifically for all the other pieces to join into. Even where the hardwood doesn't change direction. I think it also helps to keep it running square, having a piece laid square in the doorway.

A wood reducer to match your flooring should work nicely. If no one has one, they should be able to make one out of wood stock to match. It might cost a couple of bucks, but it shouldn't be too too astronomical.

I don't have a picture (I can grab get one if you like), but I did the same thing in my current project - new wood floor in the kitchen going right into existing in the dining room. The floor installer feathered some of the new boards into the dining room floor so it looked continuous, then I had all the existing floors sanded and refinished and stained the old+new 1 color. The result is a transition that looks completely continuous and uniform. Of course I had to refinish all my existing floors to do it. If you don't want to do that the only thing I can imagine working is a perpendicular strip to edge the new and old. It'd be impossible to match the old stain with new perfectly so you'd need something to separate the two. I have a spot in my house where the boards are mismatched so whomever installed it back in the day put a strip. I attached a picture of that.

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.