There is no special "archive" where certain content is set aside and stored apart from the active forums if that is what you're asking. Every single post remains exactly where it was located in the old forums.
Photo gallery posts, or photo albums, are located wherever they were previously located in the old forums. The pictures came across jut fine, with two changes:
(1) they are no longer presented as a slide show, just a collection of attachments. The attachments are not embedded either.
(2) the picture captions were lost.
I have not come across a "favorites" or "add to favorites" feature. IF there is no current list of favorites, my guess is everyone's previous list of "favorites" was not carried over, i.e. lost in the migration. I shall ask the support group about this to make sure I'm not in error. I have a sneaking suspicion the reply will be that you can use the "like" feature in the same way you formerly used the favorites feature. Your profile provides a couple of ways to retrieve a list of your liked posts & topics.
-G