It's because the "may", a modal verb, is omitted. Think of it as a request: "(May) God help me."

It's called "present simple subjunctive", which basically means the base verb doesn't change for he/she/it (or in the case of "be", it doesn't change at all). "God helps me to survive" is a fact. "God help me to survive" is a wish. Quite an important or urgent wish. You can understand it as "(May) God help me to survive".

They both make sense, however the 1st one, "God help me to survive" , sounds like a plea. As in "Please God help me!". "To be blessed" means 'to be favored by God'. Blessings therefore are directly associated with God and come from God. Thus to express a blessing is like bestowing a wish on someone that they will experience the favor of God. "May you have a blessed Christmas", therefore can also be translated as: "May you experience the favor of God during this Christmas period." When we say "God bless you...", we are saying "may God bless you". It's just quicker to say. You are probably right, your friend means to say "God helps me to survive"

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you are right your friend should have it either as God helps me to survive or God, help me to survive!