@vodot There’s an open bug for the search issues. The next release of NodeBB should address the logout issue in most cases.
The logout issue boils down to the fact that anonymous visitors, including Google crawlers, get a session, which is stored in the database. To conserve memory we limit the number of sessions. Sometimes, randomly, a regular user’s session is deleted from the database, thus the logout. In the next version of NodeBB, anonymous visitors will not get a session. The number of sessions in the db will go from hundreds of thousands to thousands.