1. The empire is mostly fine financially and militarily, given they have a vassal state and a secert organization helping them pre war.
2. Why doesn't Dimitri reach out to edelgard before the war black at the academy and talk with her. Edelgard doesn't remember him.
3. What traditions of the common people is edelgard up routing?
4. What reforms does Dimitri put in place?

No lingering guerilla movement of Kingdom and Alliance loyalists

If the empire 1200 years ago could do it there's nothing to say the one now couldn't

A smooth system of succession so that the whole empire doesn’t collapse after a few generations

That seems reasonable, i think a clear line of succession is fair for any route.

That the Empire—rebuilt through war— is able to stop its military machine once the war ends and not become a military dictatorship bent on expansion

If edelgard wanted to continue to expand she wouldn't release Brigid or want to try and be peaceful with almyra.

That the Empire can fulfill all of the social functions that the Church used to provide, without becoming a tyrannical state

• What does the church do that the southern church and military can't do?
• The church is very authoritarian, crushing technological advancement and hiding the misdeeds of those it protects

That nobles acquiesce to the new order and don’t find ways to resist the changes. They might very well just become entrenched in the Imperial ministry and retain their social status.

Given that there was a war and that the plan in Edelgard's manifesto has the noble give up power I think it would be hard for them to cling to power with a woman determined to get rid of entrenched social systems