Is anyone else dying to get to Garlemald?

[Cilia]

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Debatable. The duo share only one scene together and very little dialogue - they are together briefly when we encounter them at Ok' Zundu. That's it. Regula does seem personally protective of Varis, but whether it works the other way around is unknown - Varis does not speak a single word to Regula on screen. It's rather apparent that Varis trusted and placed great faith in Regula's abilities, but whether or not he personally cared for him... well, that has yet to be shown, childhood friends or not.

Side note: I agree that it was a shame Regula was killed off. He could have very easily been a bridge to a lasting peace with the Empire, or at least an opportunity to try negotiations that aren't necessarily aggressive. It really is too bad he had to go full General Leo, but... fanservice.

Varis showed no hesitation in denouncing Zenos, telling Elidibus that for him to mourn his death would be nonsense. He also makes it quite clear that he had no intention of letting Zenos succeed him as Emperor.

Why did Varis put Zenos into the position he did, knowing who and what he was...? Well, that's the driving question, innit? If we're to go with the most optimistic possibility that I can fathom, he did so in the hopes that governance would mature him into a worthy successor. The worst would be that he was equally interested in Aulus' theories, but did not want to be seen as a crackpot by the Garlean court. As such he gave Zenos Ala Mhigo because he knew it held research he would get Aulus to pursue, and was interested only in the results - Zenos living or dying, and how the populace fared under his rule, was of no concern to him. (As you like to point out, Garlemald has major Roman influence, and the Roman Empire was quite famous for its power politics.) For now, the truth remains unknown.

Varis did not send reinforcements because we accomplished our goal in Doma - liberating the nation sent Garlemald into a tizzy, and Doman shinobi encouraged other provinces to rebel. The other Legions were too busy dealing with the fallout of Doma's liberation to reinforce Ala Mhigo. (On paper, at least.)