Overheating and charging issues :(

I would highly suggest you replace the radiator, if it is rusty and leaking there it could be untelling what kind of shape the inside of it is in, no matter how many times you clean it. I had a similar problem such as yours on a 93 coupe I had one time, a new radiator solved my problem. A new stock replacement is not that bad expensive and is a easy swap, the radiator, water pump, clutch fan and the fan are the heart and soul of the cooling system. If you are confident everything other than the radiator are in correct working order then replace the radiator.
 
UPDATE: I replaced the radiator, and now the car runs cooler, BUT it brings up another problem!

I removed the old radiator and inspected it. it was absolute trash. and it was so full of junk that it actually weighed 1.4 lbs MORE than the other one! completely empty, both aluminum.

I installed it, filled the system, ran the car, car ran fine until i heard a loud hissing sound under the hood.

I looked around and discovered coolant almost shooting out of the weep holes on the water pump! coolant everywhere, dripping like crazy.

Even when i shut the car off, it continued to leak out!

Whats the deal here guys? I cant handle all these problems much longer. I am a full time student and work part time, i dont have the money to keep dumping into this car.

Im about two seconds from making a CL ad for it.
 
I feel your pain man, been there, done that. You probably may as well do the water pump. You may need to do a search put I would most definitely flush the block while I had the water pump off.

Or you can CL it, that would be your call.
 
I have a haynes and chiltons manual. I can change the water pump myself, its just a depressing situation because im taking the city bus to college now.

I need this car to work, i bought it because i love mustangs and 5.0s are great, reliable motors. but this thing is turning into a money pit.