is catherine alive or what?And does aliana become a vampire?

Katherine is alive and we find out about it in the third book of the series The Fury.
If you mean Elena she does become a vampire at the end of The Struggle but we figure it out at the beginning of The Fury and she kills Katherine.

Katherine is still alive and elena does become a vampire

Elena doesn't kill Katherine ,Elena became a vampire at the end of season 3. Katherine fled early in season 3 and hasn't returned yet! I highly doubt that Elena is gonna kill Katherine when she returns!!!