Do you just wash your dishes with hot water and no kind of soap or detergent?

No? Water is a "chemical". The contents of your digestive tract would probably sound scary to most people as well (hydrochloric acid in the stomach, chenodeoxycholic acid in the intestine, among others).

Not really. The surfactants/detergents get removed during the rinse cycle. The concentrations are also relatively low. Dishwashers often have a "rinse only" cycle so if this is a concern for you, run one of those after the main cycle.

Running a second rinse cycle will still put you ahead so far as water consumption, because dishwashers use much less water than hand-washing.

Tossing water soluble chemicals over dishes in a hot water jet, and in a machine that rinses with normal water afterwards.

I wouldn't worry too much about it. I do rinse my dishes with cold water before use after I take them out of the washer though.