I cast a spell, my opponent cast Counterspell, i play Twincast on his Counterspell and use the copy to counter the Counterspell. Would this be correct?
In general, when Twincast resolves, if you copy a spell that itself can target any "spell", any "instant or sorcery spell", or any "spell with a single target" (such as Counterspell, Cancel, Wild Ricochet, or Swerve), you can have the copy target Twincast, which will still be on the stack as you do so (C.R. 608.2c, 115.1a, 112.1). Soon after, Twincast goes to the graveyard as the last step of resolving, making Twincast an illegal target for the copy (C.R. 608.2k, 608.2b). And a spell with targets will fail to resolve if all of them are illegal (C.R. 608.2b).
In general, when Twincast resolves, if you copy a spell that itself can target any "spell", any "instant or sorcery spell", or any "spell with a single target" (such as Counterspell, Cancel, Wild Ricochet, or Swerve), you can have the copy target Twincast, which will still be on the stack as you do so (C.R. 608.2c, 115.1a, 112.1). Soon after, Twincast goes to the graveyard as the last step of resolving, making Twincast an illegal target for the copy (C.R. 608.2k, 608.2b). And a spell with targets will fail to resolve if all of them are illegal (C.R. 608.2b).
twincast resolves, it copies counterspell and you redirect your copy of counterspell into your opponent's counterspell
See also this thread, this thread, and this thread.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules