#3. Extra Seat of the Slain Theocracy has the title "Certain Death" which could be a skill/talent like Ainz's GOALID. But since Ainz has WCI's and a revival ring, she's probably not a serious threat. It'd be worse for the Slane Theocracy is she's exposed; Clementine says a Dragon Lord would immediately destroy their country if it discovers her existence.
#4. Just speculation, but his "alliance" with the Empire brings stability to the Kingdom, which he already controls (Renner & Eight Fingers). Also the alliance brings the "just cause" Ainz discusses in Vol. 9.
The Empire attacks the Kingdom every year for some bogus reason, but this year they're declaring the sovereignty of Nazarick. So on the surface Ainz/Nazarick is still playing by the rules everyone else has set.
#5. Assigning Momon as governor achieves a few things in one move:
Momon's basically the watchdog of both sides of this brokered peace; his positive reputation prevents any potential uprising since the people trust him.
The residents also realize fighting Ainz is a losing battle as Momon can only handle one, Albedo or Ainz. (That's why he's a hostage).
Recruiting Gazef would give Ainz/Nazarick more legitimacy.
Momon's appointment also keeps other countries - that would oppose an undead ruler - in check. Anyone who conspires against Nazarick will be seen as the aggressors and the ones responsible for disturbing the peace. Momon's reputation makes Ainz's appointment more than just a goodwill gesture, it's a significant concession for peace.
#7. Even though Ainz mostly follows Demiurge's lead, some of his actions/mistakes reinforce the Guardians high evaluation of him. Like his stupid plan to reveal himself as Momon to gain more fame is the only reason he can govern E-Rantel peacefully. And the incident with Brita leads to Nfirea/Lizzy working for him.
And the way he pulls off the battle with Shalltear secures his status as a brilliant leader to them.