Do you think we, as a community, could buy Yahoo Answers and keep it running?

No. I have no idea what it would cost to purchase Yahoo! Answers.  But, it is not likely I could afford it, even if I was one of many owners. And there is the possibility Yahoo! would rather let answers die while they own it rather than sell it. 

I could create the back end of a web app that is nearly functionally the same as Yahoo! Answers, and others could do the front end. But, I have little interest in doing so. Before Google came, Yahoo! was a leading search engine. It had a lot of name recognition, and attracted a lot of people. If we created an alternative to Yahoo! Answers, I imagine we would have trouble attracting users. 

Even if we create a clone and attract users, owners might not agree on a censorship policy. If they do agree on the policy, owners and censors might disagree on whether it applies to certain questions. Even if they agree to that, users will try to create controversy.

I, for one, don't need that frustration.

By the way, your question is in the wrong category. This category is "Sports > Running", so is about the activity -- running for exercise or for racing. I expect you will get more answers if you edit your question to move it to a better category. I suggest "Yahoo Products > Yahoo Answers."

No and I wouldn't want to.Who needs the aggravation of all these trolls.