Where is the other connection for the battery cable besides the terminal on the battery?

They don't go far, just to starter and to alternator and to a chassis ground, if you pick up a set of replacement battery cables you'll be able to figure it out pretty quick. However you might be able to get by with just a new set of terminals, if you're experiencing a bad or weak connection, that's usually where they fray at.

The negative cable, is about to split in half, the insulation was removed so that it could be secured by a metal clamp, with that being said, the more it is moved around, the more the wires inside break, I just have a lot to undo on them.

Which cable is the positive in the 2002 Mitsubishi Eclipse I just bought car and both cables are black