Can I put water in the engine coolant tank?

You can but not a lot. My advice is go to your parts store and buy the 50/50 mixed antifreeze. This already has the antifreeze / water mixed.

Check the engine compartment and the ground under the vehicle for evidence of a leak. Especially if it requires a lot of coolant to refill the system (more than say 1/2 Litre - 1 pint).

Antifreeze helps the coolant system by preventing freezing and raises the boiling temp of the coolant. If your leaking coolant always add to the system itself not the tank. The engine only draws coolant from the puke tank after the system was hot and starts to cool. Under nromal operation the cooling system is pressurized. If you loss to much you can air lock the system which can be a pain to fix if you don't cook your motor.