Was my hot water tank installed correctly?

Plumber put it in for a in floor heat loop and domestic use( which is minimal). there is no check valve in the cold water line so when the colder water gets used substantially(going to a cow waterer) the hot back flushes down the cold water line and. I also read in manual if you put in a check valve in cold supply you then need to install an expansion tank or a pressure relief valve on the cold supply. My system has no check valve and has both an expansion tank and a pressure relif valve which are installed on the out going hot water line. Why does it have to be on the cold line ? Without a check valve I shouldn't have needed either of those items. I also had a another couple gas appliances installed and both gas lines do not have drip legs. Am I out to lunch ?Maybe I just shouldn't read the manuals.

I don't know of any reason to install a relief valve on the cold water side.
Drip legs on gas supplies is some new thing they added to the code requirements a few years ago. probably because some where that 1 out of million got some moister condensation from a gas supplier so they made a law. I have never in 30 years disassembled a gas supply and found water in it unless there was a rotten/damaged under ground line that was in a wet/flooded area and water got into the line. But that line was a leaker and need to be replaced. wouldn't worry about

If you install a check Valve it becomes a closed system so if you don't put an expansion tank in the relief valve will pop frequently do to thermal expansion. Otherwise there's already a relief valve on the hwt no need for two. Also drip leg is only for drop to an appliance basically depending how much moisture is in the gas coming from your utility company plus Teflon / dope / threading oil / swarf will pool in it. It's one of those good practice things not necessarily gonna make or break your appliance