Questions and replies are saved in a database. When a question is asked, you can reply directly on the page it was asked on or (if you are an organization admin) in the Squeak! dashboard. All replies will appear in the original thread and the OP/others can ask follow up questions.

Is there an ability to approve questions before they are displayed?

Wondering about the spam that we see on other comment plugins

Yes, there is. You can approve both questions and responses fro this exact reason