On the hot water issue check your outside shower faucet. The valves maybe on and the shower head itself off. With the valves on the hot and cold are mixing causing your issue.
Don't despair you appear very green(new) things will get better don't give up yet!
Back to the genset. When I first bought my rig the tech advised me to simply disconnect the electric if I were running the genset. I agree the transfer switch should take care of this issue,but the tech advised me to unplug and eliminate any potential damage/conflicts.