In addition to everything Tyadran has already stated,
Things I like:
The hub world concept is great, it makes potential for the game have even more options for completion than even the original could have done. The monochromatic terrain and blocks I thought were interesting, as you can hide all sorts of secrets/prizes in the walls of the stage (like how those two evanescent blocks are completely indistinguishable), makes potential for a new type of gameplay we haven't seen yet. The 40 diamond requirement was an interesting way to grant access to a later part of the level after a certain condition was met. For once, players must go out of their way to collect diamonds (which aren't that common). Very well done.
The parallelism between Stairway to Heaven and Highway to Hell (ROCK ON!!) is absolutely brilliant, in that the terrain is the exact same with minor changes in block layout. Reminds me a lot of the time travel mechanic in Sonic CD. The atmosphere is nice and pristine for Stairway to Heaven and dark and menacing for Highway to Hell, which makes sense. However, I think you should switch this (make Stairway to Heaven a foreboding sky level, and Highway to Hell some weird lava paradise of sorts). I say this because take a listen to the two songs; Stairway to Heaven is actually the more somber and bleak while Highway to Hell is quite upbeat. Am I going t0o far with this? XD
Things that need work:
The music used in the intro might work in the hub world, but other than that, I would consider having the new background tracks be less repetitive.
Hub world needs a good background, and if you're gonna go with the monochromatic terrain, think carefully about what color would go best with it. Also, try and make the wall corners less jagged by choosing some tiles with more rounded edges. The rectangular look just isn't visually pleasing.
Dying in the second part of Training of Kid 1 makes you have to do the entirety of Training of Kid 2 all over again. I suggest fixing this as this is a major annoyance and something you don't want in the first two levels.
Tar Pits: The default spawn point in the level is right below where the exit telepad is, making it very easy to complete. I suggest moving one of the two.
Luna Caverns: It's probably unfinished, but it's good work so far. Make sure to fill in the large expanses of empty rooms in with something, and maybe have the telepads lead to more varied places.
A Forgotten Past and A Glimmering Future, other than the names and themes, I don't see any similarities or parallels between the two. If you can find a unique way to link the two levels together, this would be super cool.
Firewall: looks largely incomplete, and that one really tough section with the lone rubber block followed by the imp in the narrow corridor needs to be removed as it's way too difficult.
The boss: Juggernaut needs to be secret or very hard to bring into this level because he is absolutely broken when it comes to bosses. If you shoot a skull while the muzzle is inside a head's hitbox, the boss will take damage for every frame the skull is inside the boss head. Unless you want the bosses to be this easily defeated, I suggest you change that.
Tyadran also wanted me to tell you that it's better to post your files on the wiki as .ips rather than .bin for legal reasons, as direct reproduction of a game's rom is illegal or something (from my understanding) and .ips is a good loophole. We just want the wiki to be in the clear for this sort of stuff, that's all, and Tyadran can help you out with that if necessary.
Overall good progress on the mod, just needs a bit of an overhaul, and I think this could actually turn out to be awesome!