About the raid: As far as I have noticed It starts to spawn again like it does when the server save is normal. For example if server save is normally at 10 am, and first raid spawns normally at 11.08 approximately; if the extra reset happens at 12.30, the raids will start at 13.40 approximately, and so on.
About the bosses: I am not sure about all them, but if we consider what happens in the dream courts mini bosses (if it was Malofur Mangrinder day, and there is a server save, it will be Maxxenious day), I think the bosses of that day do not spawn after the new server safe, as it counts as passed day. In the example you give if the cavebear was supposed to spawn that day, it might appear again 1-3 days later, instead of 2-4