I noticed a puddle on the floor by my gas water heater. Checking out the source I found water dripping, very slowly, down the black flue at the top. No pipes were leaking No leak from the bottom. The next morning I had no hot water, and water was spraying out of the top of the water heater and running down the side I'm guessing this means the heater is shot

Based upon what I am reading, this is a similar issue I once had. There is a release valve on top of the unit that is there to protect you in case of water pressure build up. This should be a relatively inexpensive item to replace. Please do not try to fix it on your own if you are not familaiar with working on this type of appliance. Before you decide to fix it, determine how old the unit is. They usually last 8 - 10 years. Also, have you been flushing the system regulary to keep it clean? This is done by attaching a hose to the valve at the bottom and letting the water run out. This helps keep the buildup at the bottom to a minimum.
I hope this helps.