1989 Mercury Cougar - 3.8 liter - 122,500 miles

I have three questions. 1) The battery on this vehicle has a parasitic drain and I can't find where it is coming from. If this is a common problem with this make, maybe you have heard of it and know what it could be. 2) I hooked up a cheap code reader to it when the "check engine" light came on, and it gave out a code for the EGR system, yet after I replaced all 3 parts involved with this particular vehicle ( PFE system ), the code still comes up and the "check engine" light still comes on. It is possible that the code reader could be faulty ( it reads that the coolant sensor is bad when the engine is cold, yet I replaced it and that code still flashes too ), but I don't think that is the problem. 3) Does this particular vehicle have an overheating problem? I replaced many of the parts, refilled the system, and experienced repeated overheating. I bled the air out of the system through a bleeder located on the top of the intake manifold, but the overheating gage in the dash still goes into the red occasionally. Thank you for your input.