Something like suicide is hard to put a "law" on, since one the person has commited it, they are literally and figurtively done for. But yes, if they can slap some kind of law on suicide that will ultimately help prevent it, and help the people thinking of doing so, then yes.
Having laws can help prevent people from doing something in the first place. I do not think we should throw someone in jail for trying to commit suicide but we should offer them assistance try to help them get better and keep an eye on them for their own safety.
If there was a law against suicide and someone failed to commit suicide, what good would it do to put them in jail or some other nonsensical punishment. If anything, punishing them for trying to take their own life would only make that person more likely to want to take their own life. Furthermore, if the person is in a good state of mind then who are you to stop or punish them for making a decision about their life?
If you arrest someone for trying to commit suicide, you are actually giving them more of a reason to do it once they get out. Not only do you not feel life is worth living, but you now have that on your record. In England in the 1800s you would be hanged for attempting suicide...
No. There should not be laws about suicide. It is a person's choice if they would like to end their life and nobody else's business. To legislate this is to take away a fundamental freedom that we have every right to. As distasteful, upsetting and terrible as suicide is, it is a personal choice and a personal freedom.