The "water tank" above the boiler is the expansion tank. When it's operating correctly, it is partially full of water, and partially full of air.
As water heats, it expands. You either give it some place to go (the tank) or it will trip the pressure relief valve. When the system cools, it sucks in air, and you can get an air lock.
DEFINITELY have the system pressure tested. If it leaks, you've got a very good bargaining position. If it holds well, you have the single most comfortable method of heating available.
Levittowns used to be built with in-floor radiant heating. Unfortunately, over the years most systems have developed leaks and have been abandoned.
Repairing or retrofitting an old slab system can be frighteningly expensive if it does leak, and you lose headroom as you have to raise the floors by a minimum of 2". At that point I feel the best way to go isn't forced air heating that so many push, but baseboard hot water, the second most comfortable heat source there is.
If the slab isn't insulated, it will be FRIGHTFULLY inefficient. Given that there were none of the plastic type insulating materials in those days, it's doubtful that it's insulated.
As for adding additional heating capacity, you need to figure out if your current boiler can handle the extra heating load. I have a very funny feeling though, given the house's tenuous slab insulation, that it's going to be very much oversized to deal with the heat loss to the ground.