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 installed engineer hardwood floor on top of existing hardwood floor but forgot to but glue between groove. Is it going to be a problem later on? This is not interlock plank. Thank you!. Here is the product http://www.builddirect.com/Engineered-Hardwood-Floors/Maple---Dark-Chocolate/ProductDisplay_8804_p1_10071539.aspx?bdpdp=new

Before you glue to the concrete, I would like to know a few things: 1. Is the slab on, above or at grade (on the ground, above the ground or below the ground)? 2. How old is the house/slab? Old homes have issues with moisture (moisture barriers were not consistently used until the late 1980's - mid 1990's (depending on where you live). As someone who is overly cautious with hardwoods and concrete slabs, I like to be QUADRUPLE sure that a glue down is an option. And even then I would consider floating if I am not 100% sure of moisture readings. As an aside, I've read the technical specifications of this floor. I would say they are underwhelming at best. This is a 9.5mm engineered hardwood with 1.2mm wear layer. It is 5" wide (which could indicate 'glue assist' would be a good idea). This floor consists of short lengths. The longest plank will be LESS THAN 48" (states 47" as the longest plank) with an average plank length of 29.5" (less than 3ft). At $2.25/sf, it will cost more to install the product than the product is worth. I hope your installer is aware of all these shorts. Shorts make for a LONG install. And the longer it takes to install the product, the higher the price you pay the installer. I wish you luck. I really hope the 1.2mm wear layer stays attached to the 9.5mm thick plank. To do that, you will need EXCEPTIONAL humidity control. As in you need a super-duper high-end HVAC system that can have humidity added/removed with the touch of a button.

Traditionally (ie. by a pro who is paid to do things well/properly) the damaged substrate is removed and replaced. Patching is possible if there are minor spots that just need 1-3mm of fill. If the whole thing has a shredded surface then it is probably easier/faster to remove and replace with the same thickness. As G&S suggests: photos please.