The "Check Coolant Level" light

As long as you have head gasket problems your going to get that notice,, what you have is not blockage, But a serious problem that needs addressing, leaking head gaskets will take that leaking water and turn it to steam as you drive, and blow it right out the tail pipe of your car,, if its a small leak you won't even notice this until the gasket finally blows out enough to cause damage that will leave you stranded at best . they do have head gasket additives that might get you past for a very short time, I've never had any luck with them, since they just put a band aid on a severe cut

No heat to the interior of the car indicates a closed thermostat-the coolant level warning is controlled by the sensor in the surge tank, it is either disconnected or malfunctioning. cleaning the tank itself can sometimes get it working again, or look for another in a local junkyard (much less expensive than the dealer). Your overheating can very well be due to the thermostat, so changing it might solve a couple of problems-and the Northstar engines do have head gasket problems due to streaching head bolts that also damage threads, a permanent repair is to replace the head bolts with 'timesert' :

http://www.timesert.com/