Surburban SW6D 6.0 G Water heater turning off after 3 min

Quit trying to heat the water until you find out why you are getting air from the relief valve, should not happen on a full water tank. An easy test is to, with pump off and NOT connected to city water, operate the relief valve to relieve any pressure, remove the anode rod and drain the tank ( clean it while you're at it ). With the rod out turn on the pump and open a hot water faucet. If you get water from the faucet your wh is in bypass mode. If it comes out of the wh drain then you have a problem! ;-)