Dr. Robotonic is actually a separate character from Dr. Robotnik.He was Robotnik's obscure cousin who tried to steal his thunder by building knockoffs of his machinery, including the Metal Sonics and the Death Egg II. This would also explain why he is smaller than Sonic himself in this game.
The Sonic Clone is still alive.It showed that it survived its encounter with Sonic, agitated, although the fate of it is not shown afterwards.
The eighth Chaos Emerald is actually a cloned Emerald.After beating everyone else, Robotnik (or Robotonic) promptly clones your character, presumably Sonic, for a Mirror Match. Upon defeating them, you then get the eighth Chaos Emerald. Considering everyone has Emeralds except you, as you don't start with one on your person, there's the chance that one of your Emeralds was cloned as well. Why the rocket needs eight Emeralds to begin with if there were only seven for real, however, is a different question entirely, unless your character was cloned in transit to reaching the rocket and thus conveniently got an extra emerald to help with the return trip as well.
There is no eight Chaos Emerald.The game presents eighth emeralds simply to match up with the eight players and to act as a checklist/progress indicator during the results. The character you select doesn't actually have an emerald to start and is fighting everyone else for theirs. When Eggman arranges the mirror match, your character is merely beating the snot out of the clone Eggman made.
The eighth emerald is one from another set/The set of emeralds in this game is entirely separate to the standard set of Chaos Emeralds.It's been shown across various different games that Chaos Emerald come in different sets with different quantities per-set, with games like Sonic 1 and the majority of the Game Gear titles only having a set of six, Sonic Labyrinth having only four and Sonic Spinball having as many as 25. It's possible that one of the emeralds is from a different set of emeralds, or that the rocket is using a separate set of emeralds that was easier to locate at the time.