4. My secondary thought, to save energy, was to shut off my water heater when I am not home. Does anyone know how long it would take a water heater to warm up after sitting for a while. Obviously, in the winter months would take longer then the summer months. With the rising costs of just about everything, including energy, I thought this would be a good idea to save some money and do something good for the environment. So, should I just go with a simple timer or make something more elaborate?
Depends on how long you are gone.
A day? Probably better off to make sure it is insulated and just leave it on.
A week? Depends on how well it is insulated, size, wattage, etc.

1 pound of water takes 1 BTU to raise 1 degree Fahrenheit. 8.34 pounds = 1 gallon.

How cold is the water and how hot do you want it.

Something more elaborate-- Use Solar to maintain or as a pre-heater. But that involves plumbing.