You are right about the car being light. I made it lighter in attempt to compensate the rotation inertia which was too big to my taste and made the steering inaccurate. However the flipping over can be related to the car's hitbox: if the suspension travels too much, I think the car bottom can touch the ground, causing issues. However making the hitbox small makes the car fall through the ground if you jump on it, and allowing suspension to travel less also makes it difficult to travel on rough terrain and doesn't allow to compensate the car's attempt to do wheelie when you accelerate or other unhorizontalness. So... it's really not that straightforward and needs many adjustments.
As for the camera rotation, it's already oriented in the direction of the car when you enter the car, so I'm not really sure what's wrong with it now from your point of view.