Due to being Dummied Out, Sonic 2's Hidden Palace Zone is literally hidden in the code. (albeit without most of the graphics).
For that matter, the level's music (accessible in the sound test) is a truly mournful funeral dirge. As it wasn't in any version of the beta (Its music was originally that used for Mystic Cave Zone 2 Player in the final game), it was obviously composed for the sole purpose of giving the unused level its own theme to stop it crashing. A theme which represents the creator's sadness about the loss of the level, its presence in the sound test ensuring the level could never be forgotten.
That makes no sense. You don't need to compose a whole new music theme to prevent a game from crashing. It was clearly meant to be used as Hidden Palace Zone's BGM and was composed at some point in Sonic 2's development posterior to the betas we have, but in which the Zone hadn't been scrapped yet.
In the iOS/Android Port, you find the Zone by falling in the place where the infamous spike pit resided. The last place you'd expect to locate it!
Metropolis Zone contains starfish-like Badniks that explode and spread shrapnel. However, when they explode, there's no animal left behind. Conclusion? The starfishes are obviously some sort of proximity/timed mine made to look like a Badnik. When they detect Sonic, they move in; a timer (5 or so seconds) triggers the explosion.
In Hidden Palace Zone (A level that was removed from the final game) one of the giant emeralds is covering a tube that you can roll in, leaving you to wonder why it's even there. Apparently, the emeralds were originally intended to be breakable objects, meaning you were actually supposed to access that.
The reason why Robotnik can seemingly outrun Sonic to his Death Egg Robot? Because Sonic lets him. He's too noble to kill Robotnik, so he just settles for destroying his machines and foiling his plans. And he won't confront Robotnik unless it's a fair fight.
Alternatively, Robotnik has realized he must Run or Die, as he is unprotected and less than a meter away from the fasting thing alive, that put up with almost a dozen of his contraptions and an Evil Knockoff. Robotnik's ready for the last stand, and he is running faster than he ever has before out of pure fear(or determination.)