BMW Repair: Parking Light...ABS,BRAKE,and DSC Lights, bmw owner, new bmw

Question
First,

I am new BMW owner as of Thursday...2000 323i
94,XXX miles.

When I park the car is the select lever light suppose to stay on?

Second,  I have already had to change the battery.
My fault...I didn't check when buying.

However, at times the ABS, BRAKE, and DSC lights come on every now and then.  But when I drive it it seems fine...If I drive a block or two and turn the car off an on...they don't come on.

It only seems like that they come on if it has been sitting for a few hours without running.

Answer
Congraulations first off BMW's are a fine auto.My first thought is a question though,and it is did you get it from a dealer or was it a private sale?
The problem sounds like a speed sensor as you have to drive the vehicle to set the light.The problem should be checked out.