The gas cap turning the light off for a time indicates you may still have a small air leak in the emission system. Could be a line on the charcoal canister. Have you been given a fault code? P0447 is a general evap code, that in most cases won't effect drivability.
Any loss of power? Plugged Cat converter on older units is a concern.
Broken vacuum lines on the heater control box may be causing both the no heat & SES light concerns.
If this doesn't help I can only repeat what I told Customers when they called the GM store for help...hold the phone a little closer to the problem.
"Any nation that can survive what we have lately in the way of government, is on the high road to permanent glory."
ďChange is the new normal, if nothing changes, nothing is normal, everything changes, everything is normal.Ē