My car's over heating and losing water. 2004 Suzuki Verona. Is this the thermostat?

Yes, it could be the thermostat, but overheating may also be caused by many other things. Ensure engine tune or other mechanical disfunction is not contributing to the overheat problem.
Replace the thermostat, but if overheating persists I suggest you carry out the following checks:-
1) Check coolant system is not leaking fluid due cracked/perished hose or hose fitting, leaking water pump etc,
2) Check engine cooling fan/s are operating as required when engine temp rises above cut-in threshold - check fan control relay is ok,
3) Check for collapsing radiator hose on suction side of water-pump when motor revs raised above idle.
4) Check coolant reservoir pressure cap is serviceable,
5) Check coolant system is properly filled - carry out any bleed off procedure specified to clear any air locks- (ensure heater core coolant flow is turned on).
6) Check condition of radiator core:-
i) for blockage of air flow to (bugs/grass etc),
ii) for core internal blockage to coolant flow,

Likely not the thermostat as they rarely go bad could be your water pump going bad you will see as it will leak coolant on the ground. also bad fans or radiator will not cause leaks just overheating. If you have heat its not the heater core so you could have a failing head gasket which is burning the coolant in the exhaust which is a worst case costly scenario. For parts I recommend these sites before you get repairs in the shop with high labor costs: http://suzukicarparts.com/parts/2004/Suzuki/Verona/S?siteid=214820&vehicleid=187313&diagram=F753030&diagramCallOut=9 or visit http://www.bestshoppinglot.com/