Toyota Repair: Alternator and connection wiring, elec sys, pro mechanic


Question
1995 Corolla DX, 94800 miles  1.6 engine.
(I'm NOT even a hobby mechanic but I'm handy and can/did read a Chilton manual while doing this ...)
Replaced the altn. on Jan 30, 2005 (All elec. sys died while driving 1/29. Got a jump made it home, took advice of autoparts store guy that this was the problem). Thought all was fine, belt tight, recharged battery before starting, all connections appear solid.(This was a slightly different altn. than the factory style New =(BOSCH HD: 70 Amp Engine; Designation (4AFE)).  Now 3 weeks later 2/19  (basic city/expwy driving +/- 500 miles) battry light comes on. Get home, check and see the top screw-based connection wire(generator ?) is RED-HOT and glowing, covered in ash along with the bolt on the alt. and some wires/casing is FRIED! (the connect is still there and most of the wiring is attached (but singed). The other two (2) plastic plug connections  are fine.   
1. Is this a bad alternator?
2. How hard is it to replace these wires, which I trace to the back of the engine? (This is the big question since funds are limited at the moment so a pro-mechanic is out)
3. Do I replace the alt. (given the bolt burn) anyway?   4. Does this have ANYTHING to do with the battery and its grounding (autoparts guy assumption [quick call]). Can send a jpeg photoif that'll help.  
Thanks for your attention.

Answer
It sounds like the nut on the alternator connection may not have been tight,causing the overheating of the connection, not sure what is going on here, the battery won't cause this to happen, I can send you a wiring diagram but I will need an email address.