My Radio is still on

Your antennas are grounded so the radio being grounded through the coax isn't uncommon , your feed back sound from your cd player is most likely coming from the power supply you can try a noise filter in the power wire , or run a power wire straight from the battery be sure to include a fusable link if you go that route

 

http://www.amazon.com/Pyramid-NS12-InLine-Noise-Suppressor/dp/B0007V5X4U

 

Have you had the SWR checked and set on the antennas ?? That is something that needs to be done with any antenna.. if you have had it checked and it's good then it is possible that the warning light in the radio isn't right

 

I would run power to the battery and find a better ground source even if you have to run the ground to the battery also.

 

Those two things are not related.

Firstly, the radio itself is likely grounded through the chassis of the radio itself. So if your antenna coax is grounded at the antenna itself (highly likely), then the radio will still have a ground connection through that path. It's not really an issue.

As for signal degradation when your CD player is on, there could be many reasons for this. First and foremost is that your CD player may be using a switching power supply. Most switching power supplies will radiate harmonic frequencies that create noise in the CB frequency band. There's really not much you can do about it, short of finding a CD player that doesn't affect your reception.

Personally, I don't need to be concerned about anything happening on the CB beyond my sight distance. I usually keep my RF gain turned down to half scale or less. I only rely on the CB for other drivers who are passing me to let me know about lights that may be out on my truck, or something similar that might be wrong with my truck that I can't see or hadn't noticed yet.