Like you I have a 2005 Aveo purchased new, and I also have 2 daughters who drive, so here's my .02. The thermostat cracked (hairline) and started oozing coolant, just like mine did. A bit early for that at 40K, but it happens to all of the plastic ones sooner or later, just like clockwork. The coolant went low over some unknown amount of time, and was way too low on the day your daughter drove it. She didn't notice that the heat gauge was pointing due North (why would that not surprise me), and so it overheated badly. At that point the thermo housing melted and, based on what you've described, some other (more troublesome) things happened as well. The days of the V8 Ford at the top of the hill getting cooled down by the rain are over. Modern engines do not want to be badly overheated. Period.
Now, that being said, there are some things that you've described which may be outside of the engine overheating. As the original owner, what is the full oil change history of this vehicle? Every 4-5K, or something other than that? If the oil-change history is rock solid, then you MIGHT consider doing whatever head gasket/milling, etc. that is currently needed. But if the oil has not been maintained properly, then you might want to consider buying a new engine, if you really want to keep this vehicle for a number of additional years. I believe 2.5K or so gets you a new engine with a year warranty. Maybe some of the other guys have a better take on the current cost of a new motor. I know it's tough to walk away from all of the $$ you've already tossed into this, but you need to know when to fold 'em.
As previously mentioned, the leak down test (done by someone who knows what they're doing) will give you an indication of the engine's current health. Good luck with it in any case!