>First - while driving, I'm listening to the radio, and I plug my
>cellphone =
>charger into the cigarette lighter to charge the phone.  All of the
>sudden =
>I'm getting truly weird spacey noises on the radio

Cellphone chargers can generate quite a bit of radio noise.

>Second - While not driving, I plugged in my clock-radio in the evening
>to m=
>y (cheap) inverter and thence into my extra battery.  Set the clock,
>but in=
>  the morning it's half an hour fast.

The clock relies on accurate 60Hz power for it's timekeeping.  Inverters are rarely accurate.  The easiest fix is to get a battery powered clock.

Bill