IANAL but I believe that,

Any country can charge anyone as long as its laws say it has standing to do so. Having your citizens harmed is a common reason.

Yes, there are international agreements regarding copyright infringement and regarding extraditions in general. In general (and again, IANAL) I think it's common for a country to accept to extradite someone if the alleged crime is also considered a crime locally.

I have no idea regarding the latter question :)