How to implement question/answer functionality with following feature?
Well, while the Answers module does not support this entirely, it does provide some helpful functionality. (FWIW, this has been an open feature request for some time. I haven't gotten around to it ... but if you end up implementing it, I would love to integrate it.).

In particular, the Answers module allows you to programmatically "lock" questions, meaning additional answers are not allowed. You can also extend the module with the Best Answer module (which, naturally enough, enables question authors to select a Best Answer). The Best Answer module already provides an administrative setting which, if set, means that questions are automatically locked after the question author selects a Best Answer.