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Darkrai cannot be found in Black 2. (Or Any of the BW, BW2 games). You need to either transfer from a previous generation that has Darkrai or ask a friend.
Darkrai is not a legendary Pokemon check in the Pokemon Ultimate Handbook and go on Darkrai and it doesn't say legendary under it's name.
Sadly no, but u can try using an Action Replay to capture a Shiny Darkrai, All You Have to do is just download the Action Replay software.
Yes, Darkrai is a Legendary Pokémon.
You can't catch Darkrai in Pokemon FireRed, it is a 4th generation Pokemon so therefore unavailable in any of the GBA Pokemon games.