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.

based off that picture, couple of things. 1st. not oak. it looks more like Brazilian cherry. Second thats a prefinished floor. quite possibly solid 3/4 but could be engineered too. no way to really tell based off that pic. that threshold at the carpet is known as a header. in order to keep the flow of the floor when adding new wood would be to feather it in as glennsfc said. it can be done. but does cost more to do. you could leave the header and then just add flooring into that room without feathing it and would save you some, but lose the flow/continuity of the floor. Finding the same product might be hard, you could probably find the same milling size/species of floor, but the color may be hard to match perfectly. So the option would be to add raw unfinished flooring, and the refinish everything. that would help get a consistant color, could even stain it lightly to help out. All this being said, should be done by a good professional, lots of things that require a lot of skill to be done properly.

Hi there! We're excited for your installation and happy you chose such a beautiful floor! Just to clarify a few things, the installation guide pasted above is for our cork flooring, not the solid bamboo, and they install a little differently. Our solid click bamboo flooring as well as our solid tongue-and-groove bamboo flooring is 100% warrantied to be glued down (as well as nailed down or floated). However, if you're planning to glue-down over the existing hardwood, it's true that you'll need to either sand off the existing finish or add a plywood subfloor on top of the current flooring. If you need any more details, you can find the appropriate installation guide below, or you can give us a call at 888-788-2254 and we'll hook you up with a bamboo installation expert! https://www.calibamboo.com/bamboo-floor-installation/  Best of luck! Can't wait to see photos!

Please do NOT install over hardwood. I don't care if it is glued down over concrete or nailed to plywood. Vinyl and wood FINISHES do NOT work together. In fact the chemical transfer (and this is the LEAST of your worries!!! ahem!) from the wood finish to the vinyl is almost 100% guaranteed. That chemical transfer = heavy staining of the vinyl. And heavy damage to the wood floors underneath. Which renders BOTH floors unusable. And if the new owner finds out about the damage to BOTH inside of a year (or two...depends on your State's liability laws) you will STILL be on the hook for the damage/removal/replacement. The BIGGEST issue is NOT the staining - when dealing with glue-down hardwood over concrete. The BIGGEST issue is moisture damage and mold/mildew contamination. Concrete breathes and gives off moisture. The adhesive used to glue the wood is a moisture barrier but it never really 'cures'. It stays flexible. When you put vinyl over the wood you CAP the moisture. You TRAP it. That bit of moisture in the GLUE then soaks into the wood...that wood stays soaked and NOW you have huge amounts of mold growth. The chemical staining of the vinyl then SPEEDS UP. Instead of taking 5 years to stain the vinyl (over plywood subfloor) the soaked wood causes the chemical staining to occur in 1-3 years. That's when you pull up your vinyl to find the soaking, molding, useless mess. Now you have to do it all over again but this time with MOLD REMEDIATION costs added in! It's your call. But the installation instructions clearly state not to do it. They don't do this to p!ss off customers or to cost the homeowner more money. They do this to PREVENT irritation and to PREVENT greater costs later on. You wanted vinyl. You currently have hardwood. You will need to pay the piper to get this done properly. Of course if you used laminate you wouldn't have this issue. You could have run the laminate right over top of the hardwood without issue....just sayin'.