How do you know that the script is open source, if you don't know the license?
In general, a piece of work (the source code) belongs to the person that produced it. Even if they don't put a copyright statement in there, it still belongs to them. Proving that in court is a different matter however.
Depends. If you make additions/modifications, then you would own those, but you wouldn't own the entire product, so they would (legally speaking) be quite useless. If you rewrite all the code, then you're probably safe, although I'm not a lawyer.
Usually, small cases are never tried in court, so you may not have to worry about any of this. However, if you make money from it, it could become a problem for you. I would try to figure out who made the code and ask them to license it to you, before proceeding.