I often mark useful post as a favorite for future reference. Are questions and answers on the site permanent or are the old ones deleted after a certain amount of time?
Questions are not automatically pruned. However, users with over 10k reputation can vote to delete closed questions, which removes them from the view of anyone under 10k reputation (those with over 10k can still see them, and all*, deleted posts). So nothing is ever really gone from the system, even if it's marked deleted.
* There are a handful of exceptions where posts are indeed permanently excised from the system, but this is exceedingly rare and only happens in extreme cases.
Questions and answers are permanent unless deleted deliberately.