...does the search engine search the forum...
No, not at the moment. It will do some point soon, once the more major bugs have been cleared.
Also do threads on this forum get deleted after 3 months like on the old one or has that changed now?
They will do but I haven't written that part yet. Although thinking about it the main reason we did that was because the hosting we had at the time only let us have a certain amount of space for the database, so I wrote the script to trim it down so we wouldn't go over it. Nowadays we have a lot more space and control over the hosting so we could probably get away without it for now. That said, the less that's in a database the faster it will be so there's arguments for and against.