Hi, One of your problems I have had in the past.
When I bought my 93 318is, there was a constant Crackling noise that would never go away... even when you pull out the key. Plus the previous owner mentioned that he bought new battery because his old one died a few times.
The fix for me was to remove the LOWER dash cover under the steering wheel and "unplug" one of three wires conected to a small speaker. This fixed the noise problem.
After I ran a diag test on the car... error message led me towards voltage regulator problem... so I replaced. (Voltage Regulator cost $52.00 plus one hour to install)
No problems since...
Hope this helps at least ONE of your issues.