Some of the wires have a see-through, rubber connector on the end of them. Can I cut the wire below that and then hook up the wire that way?

Also, can I cut the black ground wire under the metal U-shaped part and still use it?

Yes, you can. I did. I cut the connector off and soldered the connection. If youre just gonna wrap the wires together, dont cut if off.

There should be no problem removing the ring connector on the ground wire, but why would you? Its easier to just slide it under a bolt and tighten the bolt directly onto the chassis......

Well I have to use a harness b/c I have a Tahoe with Bose. And on that harness is the black, ground wire that I'm supposed to connect to the ground wire from the radio. So, it would be a lot easier to connect it without that U-shaped metal piece on it.

ya, chop it off then. As long as its a ground, you're fine. The 'u' shaped part itself doesn't enhance the ground, its just there as a means to bolt it to the chassis.