Regarding if the Sport mode starts off in 1st or 2nd gear when taking off from a stop, on my
E46 323 Coupe it appears to take off in 1st gear; the way I determined this is to slowly apply acceleration from a stop (before it changes gear) and then to manually upshift, and to see what gear the car indicates it's in - on my 323 Coupe it indicates it is in 2nd gear, indicating that the gear prior to the upshift was 1st gear. At one stage it was indicating 3rd gear, so maybe it has changed the computer program as to what gear to start in.
Alternatively upshift manually to a higher gear eg 4, and then come to a stop and it will automatically change back to whatever gear it is going to take off in.