You can die by falling off the edge of the map in game. Also if you run out of rings during a Super Sonic fight, Sonic will helplessly fall down from the sky and the boss kills him as he falls.
No but Sonic is dying from a curse throughout the game and can’t even walk properly by the end. He is cured eventually but not until after it reaches the point where he is in a comatose state. In the DLC “Another Story” storyline, this condition spreads to Amy, Knuckles and Tails as well but they are cured before it kills them.
The kocos hold the lingering spirits of the ancients. Amy, Knuckles and Tails appear in ghost like states throughout the game although they aren’t dead
Sonic can drown if stuck underwater for too long. Easily avoidable as you are not required to be underwater at any point in the game and can quickly escape before this happens