2013 Chevy Spark.

Engine light was on. Heat wasn't working. Computer pointed to thermostat replacement. I was about to replace when I noticed there was little to no fluid in the coolant reservoir. So I filled it up. That's when I noticed the hose connector on the top right of the tank was broken. I think this is the second time this has happened. So I bought a new reservoir and just put it on. I have heat now. And no leak at the hose anymore. But ... engine light is still on. And I now see what smells/looks like maybe a water leak (pretty good one) when I run the heat or AC. Seems like if I'm not running the AC/heat, it's fine. Otherwise, pretty constant. From kinda center-left-rear of under hood. So ...

1) What do you think is causing the leak?
- It's pretty far down there ... so I don't know how I'd access it.
2) Should I still replace thermostat? Could that be causing leak ... backing up the fluid all the way to where it's leaking?
- For perspective, I feel like thermostat center right middle of under hood. The leak is, again, center LEFT back of under hood.
3) Do engine lights go off on their own when everything is working or does it need a reset?

One more note. I did have reservoir filled to fill line. And it is lower now by about an inch ... so I suppose that ain't water leaking. I don't know. I'm no mechanic. It did appear clear though ... and not pink. UPDATE #2. I drove all of five minutes to work with my AC on ... and the reservoir is now like 1/4 full. Sigh.

Thanks,
Matt