This video https://www.youtube.com/watch?v=IEP72wbgMFs basically shows everything, try to follow that path, the only thing's i'd advise is to not get a booster monokuma if it's in one of the places there are lots of cars, the places the video get them are about the only places i'd get them personally.
starting off, try to get the start boost, either hold x right before 1 or go, can't remember off the top of my head
in the long stretch with 2 sets of people on each side, if you're right in the middle you can hit both
as for the problems you're getting with 1/2 lane being blocked by cars, is due to being slow and hitting cars or getting REALLY unlucky.
oversteering, i found holding left/right for about a second and then holding opposite to straighten the best way, this really is just playing and getting used to it, you'll get it down eventually.
even doing a perfect run you can still be screwed by not getting enough point monokumas, so good luck with this.
tldr: keep practicing and getting better, you're not really missing anything, just my personal tips