En todo el día

Question

Can we drop en? Would it be correct?Can we also drop para from: nada dura para toda la vida?

Answer

Hola Emanuel
No. In Spanish you need the "en" in "en todo el día" in this context. 
This would be incorrect:
No han comido nada todo el día.
The correct way is:
No han comido nada en todo el día.
In English there is no preposition used, though:

You haven't eaten anything all day.
You haven't eaten anything at all today.

As for the second sentence with para, you can drop it if you want to without changing the meaning, but we tend to use it in this context:

Nada dura para toda la vida.
Nada dura para siempre.

Un saludo
Inma