Sonic the Hedgehog 4: Episode III is a fan-continuity of the Sonic the Hedgehog 4 game saga, involving the next step in the flashback sequence that the saga has done already, with Episode 'I involving Planet Mobius in general (even though there is no Mobius in the games and the cartoons are non-canon), in reference to the first two Sonic the Hedgehog games, and Episode II involving Little Planet, in reference to Sonic CD, respectively. You can assume immediately that Sonic the Hedgehog 4: Episode III will involve Angel Island, in reference to Sonic 3 & Knuckles.
Pretty much the same as all other Sonic 4 games. Running, jumping, homing attack, whatever.
Well, Sonic and Tails are pretty much the same as they are in Episode II. Knuckles, however, is also a playable character. You can play as Sonic, Tails, Sonic & Tails, or Knuckles.