The vacuum breaker prevents water from being sucked up into the hose and contaminating the water supply if there is a momentary hiccup or pressure drop in the supply and the hose is potentially sitting in a puddle.
The T&P valve on the water heater is a totally different thing - it prevents the tank from blowing up if the pressure or temperature gets too high.
If you don't have a check valve or prv (which contains one) in your water supply, then you don't need an expansion tank. When cold water is introduced into the tank and then heated, it expands. WIthout a check valve, it actually expands back into the supply out in the street. Some municipalities don't want that possibility to pollute the main supply, thus they install a check valve. WIth a check valve, you have a closed system, and heating water needs somewhere to expand into. Thus, the expansion tank.