If you press (perhaps accidentally) the unlock button on the fob twice
then the window rolls down as you describe to make it easier to get in to the car if space is tight.
2. Sure you're not triggering traction control?
Current: 2013 F10 520d M-Sport, Professional Media, Visibility Pack, Reversing Camera, DAB
Previous: 2011 F10 520d M-Sport, 2008 320i M-Sport Coupe, 2002 325i, 2001 318i valvetronic, 1998 318i, 1996 525i, 1990 Porsche 944S2