We have a hunt camp in Northern Ontario that is completely off the grid. The cabin is wired like a normal house with 240 v coming into the panel and then split between two legs and powered by a large generator to provide 240 V power to an electric water heater and a water pump. This generator consumes a lot of fuel. To conserve power we disconnect the large 240 V generator and use a small 2000 v Honda 120v generator. We have a small double male ended extension cord that we use to plug in the 120 V generator to a wall socket. We get normal 120 volt power to half the cabin which is fine to run a TV and coffee maker but not all the lights work because half of the cabin is on the other side of the panel. If we turn ON the hot water breaker, we get 120 throughout the cabin. The 120 runs across the heater element in the water heater. Are we damaging anything by doing this?

Well, first thing I will say is using a double male extension cord is one of the dumbest things anyone could ever do. They do not call them suicide cords for nothing.
Sorry if this opinion offends you, but I am not in this to make friends. I am in this to give people advice sot hey don't kill themselves or others.

PLEASE hook this up right before you do anything else. Get yourself some form of isolator or transfer switch so that you are not energizing exposed parts.

Also, it is NOT a good idea to run the current through the water heater element. There is resistance I the element so you are not getting the same power out as in. Anything plugged in on the opposite side may be adversely affected.