On the back of an Alternator, the threaded post where 2 roughly 16 guage cables attach...where do those cables go to? Can i run them directly to the battery? Mine melted right on the back of the alternator, and people have told me it was because of a loose connection?

Yes.

On older cars you can, as i have thae "charge wire" that goes straight to the positive terminal set up on my XP.

Not to sure on newer cars however, as im assumiming its in your NC, so yea, best get advice from soemone qualified