Religions would stay the same, though they'd have to be practiced in secret as the dragons would want to be worshipped. As for the Daedra, well, theres mixed feelings. Some of the Daedra support the dragons, Mehrunes Dagon and Clavicus Vile are examples, and some despise them, Sanguine and Azura are examples. Some are neutral, like Sheogorath and Molag Bal. They use their current champions, if they have them, and their cults to either help out or hinder the dragons and resistance.
The Aldmeri Dominion ignored the situation until it reached their borders, researching it but not getting involved so it would weaken the Empire. When it finally reached them they realized their mistake and tried to strike a deal where they would keep the Summerset Isles and the dragons could have Elsewyr and Valenwood. This caused the two provinces to finally revolt, weakening the Aldmeri Dominion. The Dragons quickly took over while still waging war against the Empire, Hammerfell and Black Marsh. The Sload realized what a great opportunity for furthering themselves this was and quickly handed their land over to the dragons. Their leader became the first new Dragon Priest, taking the mask of Volsung. They conquered Skyrim, High Rock and Morrowind first, reducing the Empire to just one province. They quickly dissolved into a random smattering of kingdoms. These were easliy conquered. Hammerfell allied with Black Marsh and Orsinium and together they fought, conquering the mostly ignored Cyrodill. They put up a good resistance but were eventually conquered. Alduin placed his capitol at the World-Eaters Eyrie, but intends to move it to the Tsaesci capitol city in revenge for them nearly wiping out the dragons. Pyandonea quickly dissolved almost as soon as reports surfaced that the dragons were heading South. The few Nedes left on Atmora still worshipped dragons and gladly gave in. Three of them became the dragon priests Nahkriin, Otar and Hevnoraak. The Pyandonean king, an immortal wizard, became the fifth new dragon priest, taking the mask of Krosis. The few Left-Handed Elves and Redguards on Yokuda were conquered after a grueling war and were nearly wiped out entirely. The remaining island kingdoms quickly fell into the dragons hands, including many of the Tang Mos lands. One Tang Mo leader took the mask of Rahgot. The dragons quickly returned to the old ways, though slightly modernized due to the multitude of new subjects.
Dragon combat will be minimal at first, though I intend to have a healthy mix of trickery, book-reading and fighting.
I also intend to introduce myself as the new Konahrik and have other npcs replace the old Dragon Priests. Any other questions?