From your shots there, the Mk1 shot is fine and the Mk4 rolling shot is good, but the others are out slightly of focus so it might be that the camera is struggling to focus in the low light, or it could be a slight camera wobble due to a slow shutter speed.
With your bridge camera, you've not got the option of a prime lens capable of anything like f1.8, but if you knock the ISO upto 800 and then you can get the f-stop to f3.5 or something then you'll get a higher shutter speed and you'll be able to eliminate the camera wobble.
What level is the course aimed at? Beginner/Intermediate?
If it's a beginner course, they should a) tell you what you need to bring and b) show you the basics of how to take good photos which will apply to all types of photography not just portraits or still-life.
If they are teaching you Photoshop, then they should provide computers.
If in doubt you could always phone and ask to speak to the tutor.
If car photography is your thing, then take a look at photos by people like:
Ronaldo86 on flickrMike Burroughs (stanceworks) on flickr or
GF Williams on flickrLooks through all their photos and find ones you like, then look at them and work out why you like them: is it the light, is it the angle (low or high), does the car fill the photo or is there a lot of background, what is your eye drawn to in the photo (ie the point of interest), is it a whole car or part of one?
The course may not cover automotive photograhy specifically, but bear with it, as it should teach you how to get make the most of what's in front of you with your camera.
Stuff like how to use shutter speed creatively will teach you something about how to freeze a moving car or how to give the impression of movement.
You will inevitably find someone whose daddy bought them a Canon 7D DSLR, but they have no clue how to make the most of it. Ignore the whole kit thing. You can still get great pics with a bridge or compact camera, you just need to know how to use it.
I hope you find it useful. I wish I had more time to work on my skills, so make the most of the course and keep on practising in your spare time.