No need to write off the 35mm completely, since it does have great low light gathering capabilities. However, as has been said you simply won't be able to get the crops you want with it and you won't be able to go wide enough for anywhere that there are people crowding around and you want a clear view without people in the way.
The 18-200 can do this but has much poorer low light, so you may be at a very high ISO most of the time.
You could invest in a constant f/2.8 mid range zoom which would give you a good middle ground but that would be expensive. In Nikon DX that's the 17-55mm f/2.8. Awesome lens for what you want to do, but very expensive and not worth it if you don't do this kind of thing all the time.
You could consider hiring lenses, too.
As for what settings to use? I'll give this advice just because you said you're a rookie: just use P mode unless you want a specific aperture, in which you use A mode, or you need a specific shutter speed (which I can't imagine happening there) in which case you want S mode. Basically. Many beginning photographers are brainwashed into thinking that if you're not using full manual, it's not real photography. It's true that experienced photographers often (or almost always) venture into Aperture- or Shutter-priority modes (or in some cases like long exposures, controlled lighting etc, Full Manual). But they do it for specific reasons, in order to get specific effects. Your camera will choose its aperture and shutter speed in a scientific way, not an artistic way. Start with that, and when you know you need a particular aperture, then override it. And so on. Do you know what I mean?
You will be limited by low lighting anyway, so even if you wanted more depth of field by closing down the aperture you may be compromising on noise or shutter speed a bit by getting it. So if and when you close down the aperture a little bit for that extra depth of field, keep an eye on what shutter speed it's picking to ensure is over 1/30s (when held firmly, or 1/250s if there are people in the photo you don't want blurred!) and in case of auto ISO, that it's not going outrageous (400 is good, 800 is not ideal but you can try it, 1600 is a bitta grain, 3200 is grainy as bro).
On-camera flash may create ugly looking reflections in shiny objects, which car shows will have a lot of.