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.

Choose a slate that is not flaky, or that has been cut smooth and polished. You're much more likely to get damaged hardwood from small pebbles in shoes and women's high heels than from random flakes from slate.

Hi. I did something like this in my house. I have a split level. I put Biscayne Oak from Coretec down next to oak stairs. The vinyl extends out down the hallway and into a bathroom and family room. This whole level of the house is the same. It looked the best color wise next to the oak stairs. I put the vinyl over where the tile is as there are 2 layers of tile and demo for that was costly. I am thinking to do the same floor in the upstairs hallway and kitchen, which again is all hardwood floors same color as the stairs. I am nervous to do this in the kitchen and upstairs hallway, but the bathrooms all have the coretech vinyl floor because again 2 layers of tile, and cost. I dont think it looks bad with what you want to do. I will say this, cleaning these coretec floors is heaven :) so easy

Modern means simple I have no idea what you mean by stacked unless the new floor is tile or tile look. Myabe post a pic of the new floor. I certainly would not do either of those other patterns if modern is your aim. I have laminate all thorugh my home that is from Germany , has an amazing caoting on it that my 3 huge dogs have not been able to scratch a wood floor would have been totalled by now. I have vinyl plank is out walk out it is 13 yrs old and the new ones are certainly better but mine still looks great and those same dogs are in and out of that level all the time from a dog run.What layout you have is not really staggered it is how real wood gets installed . Do you want wood look flooring or maybe something different our laminate in the main floor looks like slate and it is even a bit textured most people think it is stone.I love it because it works with my FP. @ of the dogs the other one weigh 125 lbs.