Re; Little Froggie
I honestly do not know how it works. FYI the hot water heater is in the basement of our house.
I just remember that we asked our Rov, and he told us which boiler to buy (I don’t remember his specific reasoning) or how the boiler circulates the hot water. I seem to remember that it works with pressure (from the sinks). I do know that the boiler does not turn on all Shabbos, without the incoming cold water, it does not turn on at all.