Did Alec Lightwood Die?

Alec Lightwood (Matthew Daddario) was stabbed through the chest in episode 10, and he lay dying in his partner Magnus Bane's (Harry Shum Jr.) arms as the Warlock was unable to heal him since he had traded his magic to break the Queen of Hell, Lilith's hold over Jace Wayland (Dominic Sherwood).

Does Lightwood die?

Robert tried to calm her but forgot that she was holding the Sword, and she stabbed him through the chest with it, killing him. Robert's funeral was held the following day. His body was burned alongside Livvy Blackthorn who had also died in the Council meeting.

How does Alec survive?

As Alec begins to lose consciousness, Jace pleads with Magnus to save him. Magnus admits his magic is gone and assures Jace he will take care of Alec. So basically, Alec's story ended in 3A with an arrow in his chest. We do know from sneak peeks and the recently released trailer that he does make a recovery.