First issue here is to understand that, technically speaking, it may not be ideal to call that person "my clone", since essentially it would be more of a "duplicate". He is I, in every possible sense of the word, even though, technically, he was "created" after me. As I consider that a human being is basically it's mind and experiences, then we are indistinguishable as individuals according to this premise.
If he is me, then, I 'm sure he would not kill a human being, except in a situation of self-defense. That, of course, is my case also. So, no, I would not kill him and he certainly would not kill me.
For the rest of the questions, well, I have no particular attachment to my "lifestyle". Certainly, in this world, there is room for two people "like me". Initially it would be somewhat complicated, I imagine. What would we do with the work? Maybe split the income and working periods (each one going for a day) until one of us could find another. And I would not mind being the one searching, which tells me that he certainly would not mind also.
Same thing about my name. If necessary, I even let my "clone" with my original name, changing to a new one. It would be quite interesting thing to do, really, kinda starting a "new life". What makes me think that the situation would be exotic because undoubtedly he would think the same. But for practical purposes, at least one of us would have to change the name and the other should keep it. I dunno how to solve this since no doubt both would have the same opinion. Possibly it would be by lottery.
I'm not married nor have children, but being honest, I never really had an "emotional attachment" as strong to a person that made me want either of these things. (And as I have reasonably more than thirty years of age... I guess that will not change at this point.) So, good, I have not much to lose here, and I cannot imagine what would happen if it was the case since, well, I don't really want that in my life.
It seems to me that this situation isn't as dire as you make it sound, honestly. It would be a great inconvenience, undoubtedly, because of all the things we would need to solve. But I think I would rather sympathize with him, after all, he is myself. I know what he thinks and how feels things, therefore, I cannot 'not' like him, and I don't know how to ignore what he thinks about. I literally and completely understand him, also. Most likely, it would be the most honest and sincere relationship between two people in the world. I think we would be great friends, that's the truth.
Therefore, I believe we would find a way to reconcile and follow our own lives.