In my opinion, that's pretty close to perfect. For what it's worth, this is how I would word the first sentence: "The situation that more and more car-owners don't have good driving habits means that there are a lot of traffic accidents." It's common to omit the "that", by the way, but I think it makes the sentence flow better. I might also consider changing "which will be the best ways" to "what will be the best ways". They're both technically correct, but the second variant is very slightly more usual.

The fact that more and more people owning cars don't have good driving habits causes a lot of traffic accidents. There is an ongoing discussion about which will be the best ways to make our roads safer. In my opinion, I think not only strict punishments but also other measures should be used to promote safe driving. fine - I changed cause to causes. Strictly it is there bad driving that causes the accidents, not the fact itself. But, as it stands, you say It causes. :)