> 1) to actually generate the energy (steam!)

Secondary loop can be made closed system. This reduces efficiency, but this could be acceptable considering water scarcity. Of course there would be some leaks etc. so water needs to be resupplied, but in much lesser amounts.

> 2) to cool

Not necessarily true, because primary loop doesn't need to have water (HTG, MSR, LMR reactors). HTG reactor actually doesn't need water at all and can power gas turbine directly. LMR, depending on chosen coolant, can do this as well, though it requires heat exchanger.