The Complete Super Guide (v2, more completer):
Super forms appeared in every level that you had 7 Chaos Emeralds in in Sonic 2-S&K. Knuckles went Super in every game he was in in that period. Tails needed the Super Emeralds as well as the Chaos Emeralds to go Super, and could thus do so only in S3&K. Super Shadow, and Shadow himself, first appeared in SA2, and thus Shadow has been Super only in the last levels of SA2 and StH.
Hyper forms are basically the Super forms of Sonic/Knuckles plus a Armaggedon effect. As Tails needed all 14 emeralds to go Super, he did not have a Hyper form. The only game with 14 emeralds is S3&K, so Hyper forms only exist in that game. And yes, they did flash. They also produced afterimages. Tails never had a Hyper form, to clear that up for anybody who didn't get that the first time, and didn't realize that needing 14 emeralds to go Super Tails implied that.
The first forced Super level was The Doomsday Zone, the last level of S&K. It was playable only as Sonic. In every later game with Super characters in it, you could become Super only in the final level.