Due to being Dummied Out, Sonic 2's Hidden Palace Zone is literally hidden in the code. (albeit without most of the graphics).
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.)
Oil Ocean Zone's music has a very Arabian feel to it. Quite fitting since Arabia has one of the largest oil reserves in the world.
Robotnik saving Sonic in the 8-bit version actually does make sense. In the story of this game, Robotnik plans on using Tails as a bargaining chip for Sonic to hand over the Chaos Emeralds. Since the first Chaos Emerald is obtained a bit earlier, Robotnik was saving Sonic because he doesn't want the Chaos Emerald to fall into the lava.