What is a sanitary pump?

Yes, a defective relay will prevent the pump from running.

the horizontal distance depends on the friction of the piping, however the vertical distance is different for each pump. on the nameplate of the pump is usually indicated the total head developed...

Yes. However in some application we can use a rotary type.

Yes, You pump from one pump into a second to get a greater pressure boost. Be sure that the pumps and lines can handle the pressure increase.

A heat pump's name is a bit deceiving, it's just an appliance that heats water. You still need a normal pump and filter combination to move and filter the water.