Only a human being can die. And yet, because of the fact that God was truly present through Jesus, God experienced death through him. We can say that God died, but vicariously. One question that is often brought up is how Jesus can pray to God if he is God. But recall that according to the Trinity, God has within himself personal relationship.
Relationship implies communication.
I don't know what type of communication goes on in eternity between the Father, the Logos, and the Holy Spirit. Because they are aspects of one God, I'm sure their communication is more direct than human prayer. But relationship implies communication of some sort. So if we are serious about saying that God is personal, he is involved in communication in some way. As God is the source of personality, he is the source of communication.