No, Puck hasn't died yet and there have been no announcements saying he would die in a future episode.
Laryngitis!
Laryngitis episode 18 of season 1
Episode 3, Acafellas.
Never been kissed
Season 1, episode 11, Hairogrophy
Its episode 18 called 'Lady is a tramp'
Never been Kissed, episode 6.
I'm supposing you mean when he cocks his eyebrow? If so, Season 1, Episode 10 (Ballad)
the one where he was asking people to join the glee club and he met lauren
I believe it's episode 8 - Mash-Up
No, In that episode Puck is in Juvie. Mark Salling however, the actor that play's Puck was off working on his Music Career.