Mineta is kind of like Rome without the benefit of the Catholic church though, an influential little rump state with considerable international prestige but probably very little practical political clout. I very, very much doubt that the outlying Elumian states pay any sort of tribute to Mineta. My guess would be that it's like early modern Europe and most large states are just starting to get into the business of maintaining permanent ambassadorial staff in each other's countries. I would imagine for reasons of prestige almost all of them at least try to send some kind of representative to Mineta. I think Free is right that sending embassies to others would probably be below Mineta's Imperial dignity, but I think they'd probably do it anyway, at least to important states and close neighbours. In our world Hapsburg Austria and the Papal States maintained relations with other countries after all. You need to keep an eye on people.
As to the empire retaking its former territory, well... there's a difference between wanting something and being able to do something. It seems difficult to believe that even if a new emperor was appointed, unless there was a truly catastrophic event to unite everyone behind them, that the empire will ever be its former size. Meril is supposedly on the rise, no? What do you think would happen if someone from outside Meril tried to put a pretender on the imperial throne. How would the Meriliens react to this challenge to their growing power?