It could also be said Ulfric survived three times being captured by his enemies.
By sheer luck on that third escape. It took a long since gone dragon to cause his escape.
No, he meant the Empire as a whole, and there aren't second thoughts about that. He also says it's time to try "something new", and just a change of families can be hardly considered "something new".
No, he meant the septim empire. Unless you have definitive proof he meant every Imperial empire from here on out? Sure he might have
said it's time for something new but that didn't happen. There was a time after witnessing Martin die in Oblivion that I thought that some new form of government might spring fourth for Tamriel too, but I was wrong with the Mede empire.There may not always be empires (though to be honest for this world/game series I hope there will be) but my guess is there will be for at least a few more centuries.
On the other hand though, maybe your point is why there was barely any new lore for the Mede line so far but we will have to see.