If you die, you'll return to the room where you first met Homunculus. There he'll give you a hint. Becoming trapped in time means game over. What you do during the game is, in many places, up to you. There are a few different paths to the end.
Every action has, to use an old saying, a reaction.
So try different things, they may just open something for you. So, in a way, much of the game is non-linear. I have to mention the cast of this game. You'll meet up with different generations of most of the characters. Take Mr. Eckart, the museum director, for example.