Why did my car overheat?

I've got a 2004 Sebring convertible with the 2.7. I've had some issues the past few days with the cooling system.

Yesterday my car overheated with coolant all over the driveway. Once it cooled down, I noticed that the cap on the overflow tank wasn't seated correctly. I wish I could blame it on someone else, but I had opened it yesterday morning. I assume this led to it overheating.

Looking down into the overflow tank, it appears that the tank is full. Looking at it from the side (and it is extremely discolored), I see the lines to the level that it should be filled, but I can't discern any coolant (my "former" mechanic put the green coolant in it, so it is harder to see. I will be getting a flush this week and putting in the right coolant). But, for lack of a better term, the "neck" of the overflow tank is full and won't accept any more coolant. Could there be air blocking the coolant from entering the body of the overflow tank?

To make matter worse, I'm pretty sure I have a problem with the coolant air bleeder valve. Last year the original one basically blew up. My "former" mechanic put in a replacement. I had another mechanic look at it a while back and said that he thought it was faulty. I think I finally understand what he means. When I try to tighten or loosen the bleeder screw, the entire thing turns. Not just the screw, but the metal cylinder it sits in, too. So, I can't really tighten or loosen it. The entire thing spins. I ordered a new coolant air bleeder from AutoZone that will be here tomorrow. I've watched some videos and feel that I can tackle the job of replacing it, other than torquing the bolts.

I'm not exceptionally mechanical, but being a husband and father with four cars I've had to learn a few things. Any thoughts or suggestions? I feel pretty stupid that I can't even fill the overflow tank with coolant.