Chimes didn't use the radio until later I'm fairly certain. This car being an 01 had them handled separately. 05 I think is when chimes were integrated.
OP: I should clarify, are they the units from the car. If they are scrapyard pulls or used units something could be wrong with the install.
The wire in the DRL circuit sounds like someone wanted 12 Volt when the key was "on." This is often the case with dash cameras or other after market AV accessories.
Interior lights being "always on" screams a short in the system.
I am sorry to be rude, but severe electrical gremlins are on the edge of being outside DIY territory. If you have experience or a friend with experience you can really proceed, but if you are coming in totally blank a shop is recommended. Shorts can go as far as causing fire in the vehicle. Additionally, GM is obnoxious when it comes to swapping many components that are integrated into the system, offend requiring them to be programmed to VIN match the rest of the system or they will not function correctly.
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