Purpose is part of it, yes. If something only has the applicable purpose of killing massive amounts of people (nukes), they should be highly regulated. You could, of course, just have one for decoration or because you are a war nut, or some other strange reason. But the only purpose is to kill people, and hence we regulate them.
No that is not the purpose. I can prove it because I use guns for things other than killing things. I told you what a gun is designed to do. Apparently that is one area that escapes your superior intellect. The purpose of the instrument itself is not to kill. As I said, even a gun by itself, can't kill. It also has to have bullett.
Not quite, no. We don't buy bleach for the purpose of fueling our cars. Why? Because of the properties of bleach. Purposes of items obviously have a lot to do with the properties of said items.
Sure all things have some type of purpose. A machine, which a gun can be defined as, is designed to accomplish something, but kill isn't it.