While googling for more information on a problem I had, I came across a website (I don't know if its non-profit or not) that had a question I had posted a while back. I had no idea the content on this website was being duplicated onto other websites. Do they have the rights to do so? If yes, how many websites outside the Stack Exchange network are doing this?
Posts on Stack Exchange are licensed under a Creative Commons license.
The legal page for the network lists the attribution rules. See the list in section 3, "Subscriber Content."
If you think there's a problem with another website copying content without obeying the guidelines, you can contact Stack Exchange, and they can take the appropriate action.
In the linked case, it doesn't look like attribution is being properly given - I don't see any network attribution (ie, there's no mention of Stack Exchange) and the question and answer must both link to the person who posted it's profiles, among other things.
There's not really an easy way to say how many other sites use SE or Arqade content without doing some real deep Google dives or similar. There are plenty that use SE content with the proper attribution, for instance Ars Technica does, as does Lifehacker. Heck, sometimes even I use Arqade content. (In this case, just a question that was closed but I wanted to answer anyhow)
Yes, other websites can duplicate questions and answers, as long as they follow the guidelines: see this related answer on meta.so.
However, a quick look demonstrates that this site doesn't abide by the terms. Please report this by sending a message to Stack Exchange or by reporting it on Report sites that use Stack Exchange content without following attribution rules here