No sound from CD changer, but radio and cassette work = CD changer faulty.
Intermittent radio: this could simply be a loose plug, although BMW lever type plugs are very positive in use. There is really only cable between the head and modules in the boot, so plug checking is minimal. To check those on the headunit, remove just 4 screws whether 4:3 or 16:9 monitor, slide out.
Bumps might be affecting the connections inside the radio module, which is also located right up against the rear left wing with all the other modules. Its looks daunting to remove but is really quite straightforward-take your time on re-assembly, ensuring no trapped cables (which is easily done). Search BMW BM54 to see some pics. IIRC there is also a fuse to this module, that you might check too. Its quite common to the extent there are a number of people offering repairs to circuit board soldering...
You might be lucky with the cd changer-the cassettes become faulty but are available-not a repair I have done. Check too that the suspension screws on each side are set for vertical use; mine were set for horizontal.
Shimmy-where to start! There are a lot of ball joints on the E38 front suspension, and wear often shows as a shimmy at 50-60mph. If it only occurs on braking, could be just brake discs (rotors). If you replace any joints , only use OEM, most other stuff doesn't last, however tempting the price.