I bought a 12SI alternator and kit from a local shop that came highly recommened from several people. I noticed that my old alternator has a ground wire that goes to the back of the alternator (see pic) but the 12SI doesn't have a terminal for the ground wire so I'm assuming that I elminate it? Also, the kit is idiot proofed (which I love by the way) so I can't hook it up wrong (see pic) but I noticed that one of the wires in the existing harness that plugs into the back of my alternator is looking pretty bad (it's 36 years old). What I mean by that is I can see a few broken strands of wire and it's looking somewhat dirty and old so my question is can I cut off the existing terminal and strip the wire back and reattach it in the harness? I tried to get a picture of it with my camera but it came out blury. Thanks.

Yes you can.

Yes you can.

Okay, how do you remove the terminals from the harness? Oh, and what about the ground wire?

Okay, how do you remove the terminals from the harness? Those terminals are called Packard 56 series terminals. There is a male terminal (bottom one) and a female terminal (top one), see pic below

http://www.chevelles.com/showroom/data/500/flat-b6.jpg

Disconnect battery first. To remove a female terminal from the connector body, insert a very small flat blade screwdriver in the side the plugs in, what you are trying to do is to push the small tab you see in the pic down. Once you push the tab down, then pull on wire and terminal will come out.

To remove a male terminal from the connector body, squeeze the hook part of the terminal together, then pull the wire and terminal will come out.

Oh, and what about the ground wire?
You really don't need one, the only time one is needed is if the alternator is poorly grounded to the engine.