514 - Battery Temperature Sensor Circuit Range/Performance
162 - O2 Sensor Circuit Malfunction (Bank 2 Sensor 3)
I would check the battery connections and also just charge it up, if the condition is unknown/if it's been standing unused for a while.
If the o2 sensor has a problem, then there's the connector to check and the fuse/relay for the sensor heater.. but I don't know where those are on the 500 (yet!). The O2 sensor error is probably the one causing the "limp".
As for the original problem, a dodgy thermostat does not usually affect the coolant level, so changing it won't solve the issue, unless - rarely - it's sticking closed and causing the car to overheat and evaporate coolant.
But it sounds like your car is losing too much coolant. I suspect you have a leaking radiator (get under the car after its been parked overnight and look for wet patches on the ground, or feel for wetness under the radiator area). If you're losing that much, then it has to be a leak. If the rad' checks out okay.. look at the area around the water pump.
You could also have a head gasket issue. If you have a bleed valve on the radiator, bleed the radiator (* cold system *) and see if any gas/air comes out. Undo it (not all the way out, or you'll flood the driveway) just enough for all the air to escape. When coolant comes out, close the screw and then test the radiator for gas again after a day or two to see if the gas comes back. If you keep finding air, the head gasket is KIA and needs replacing.
If you can't find any signs of problems then check that the fan comes on when the car gets hot. If you're in traffic one hour per day, the beast might be heating up... and without a fan to cool it, it could be pressurizing the system enough for coolant to be expelled, without actually boiling over.
I'm more inclined to suspect radiator (leak) or head gasket, for the amount of coolant you're losing... but check each component until you find the problem. It'll be fairly obvious when you see it.
Ralf S.