Oh, saving your game in Sonic Colours for DS is as easy as painting a happy little tree. Just find a Save Point within the game, usually marked by a glowing icon or a specific location. When you reach the Save Point, simply interact with it, and your progress will be saved peacefully, ready for you to come back and enjoy another day of colorful adventures.
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It has the autosave feature, so it saves itself while loading. You can just turn off the DS and come back to the mission you were on later.
It is found in the final boss of Sonic Colours.
There isn't one that is just Sonic the hedgehog 2, but there is the Sonic Classic Collection which has 1,2,3, and Sonic & Knuckles
On fossil fighters you cant save your game
on the game card itself.
Assuming that the emulated game is the same generation as the game you are trading to, you need to place your game and save on a DS flash cartridge, and it will act like a normal DS game from there.