Exactly when did Madara come back to life after his defeat by Hashirama? I know that Madara used Transcription Seal: Izanagi to fake his death and came back to life after a while. What was the trigger for this jutsu (Izanagi)? If it was his death, immediately he would've come back to life after death and Hashirama would've noticed it. 

It is mentioned that he had used this jutsu on his own right eye. How come a dead person's eye is a trigger for his own revival? As I understand, there won't be any movement/thought from a dead person.
Izanagi is a technique which is able to rewrite history. You take an event that wasn't favorable to you and make it into nothing more than a dream.

He set up Izanagi beforehand to be trigger a few hours after his death. Even though he was already dead, the technique still activated (Much like Itachi sealed his own Amaterasu into Sasuke's eye, and it activated even though Itachi already died).

Once Izanagi was activated, Madara's death was cancelled.