No, Puck hasn't died yet and there have been no announcements saying he would die in a future episode.
Laryngitis!
Episode 3, Acafellas.
Laryngitis episode 18 of season 1
Never been kissed
Never been Kissed, episode 6.
Its episode 18 called 'Lady is a tramp'
Season 1, episode 11, Hairogrophy
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
Puck joins glee club in Season 1, episode 4: Preggers, at the very end.