Hi I just bought a 93 325I with 135K miles that has a few problems. This morning I started it and then decided to drive my other car. WHen I switched off the ignition and removed the key, I could still hear a motor/fan sound (a humming) coming from the dash below the radio. I've never owned a BMW before so am new to how these cars behave. I do all my own mechanical work and would love to learn about these cars. If anyone knows what this might be please let me know. Thanks.
P.S. Some other issues while I'm at it. 1)
The radio only has static unless you wrap it firmly on the side, then it comes on

.
The sunroof only opens and closes. It doesn't do the tilt up thing anymore. Might that be just a switch?
Where does one check the transmission fluid in these cars? The owners manual makes no reference to it. As part of the maintenance routine, should I flush it and refill with SYnthetic?
Last but not least. I need a catalytic converter to pass emissions test. Are the aftermarket Kraco's okay?