Depends on how one defines "you". Are you the culmination of your life at the current instance in time, or do you see "you" as a simple label placed upon a life form? In one case, that you isn't exactly you. In the other, it is. Would it be legal? No.

It really depends on how the whole time traveling thing works. For example if I went back in time and kill myself the me that killed me would still exist because the action that I have taken has created an alternate reality. So now this alternate reality exist out of my reality so whatever I do in their reality won't happen in my reality. Or I would cease to exist.

You wouldn't exist anymore so the future never happened cause you died in the past

It'd be impossible to go back in time to kill someone specifically and have that affect the current timeline. If time travel involves multiple universes, the original timeline will still exist. If time travel is linear, killing someone you specifically target wouldn't work either. As soon as you killed them, they would be dead and you would have no reason to target (or knowledge of) that person. Thus, they would not die. Killing yourself in that second scenario would have the same reset result, since you'd have to be alive to go back in time to kill yourself.