My take on those questions.
1. Are the Aedra or Daedra more powerful? The Aedra always seem to make rules for the daedra, (i.e. the daedra can do nothing to harm mundus as akatosh told Alessia) and Akatosh totally kicked Dagoth Urs A$$. But at the same time, Boethia turned one of the Aedra into Malacath. (which turned the orsimer into orcs) Which leads me to my next question.
Firstly, it depends on the locations. The Aedra, who contributed to creation, "Mundus" became the laws of the Universe. If the Daedra cannot do something in a certain place, it's that the nature of the locations, and so too thier own nature forbids it. Within the material universe then, the Daedra are not all powerful.
Secondly, you have your villains mixed up. The Nerevarine was the hero who kicked Dagoth Ur's A$$, and that was without the help of the Aedra or the Daedra, though some may contest this either way. Personally I find both the Aedric assistance and the Dagonite assistance proposals rather late, and unnecessary.
2. Are certain Daedra more powerful than others? None of the other Daedra seem as bad ass as Boethia and Meruhnes Dagon. (i.e. as you find in the Shvering Isles, the daedra feared Jyggilag had become to powerful so they made him Sheogorath.)
SI gives the impession. Mythically, it's whoever has enough worshipers, and each to his/her own sphere. I'd say that Dagon could not tell as lie better than Boethiah, and Jyggalag could not host a party better than Sanguine. Pardon my simplicity though, I'm sure there are much deeper and epistemological drives for Daedric and Aedric behaviour.
3. Moving away from the questions of Aedra and Daedra, when did the Akavir, uhh snake people (Taescei?) live in or consort with the Empire. I recall a book in oblivion that was based on a challenge between an akavir and an Imperial; both of royal blood, (2021 Morning Star i think)and ive read the breaf history of the empire and nowhere does it mention peaceful dealings with the akavir
We know little of Akavir. One of the, various misjudged endeavors of the 2nd Empire of Tamriel was to invade Akavir. They lost. And there have been, afterwards, various endeavors from Akavir to conquer Tamriel. Somewhere between the eras of the 2nd and 3rd a shared sense of interest grew between the two, and the late 2nd Empire employed various Tsaeci to varying degrees of important positions in it's hierarchy and bureaucracy.
The duel that you alluded to was between the Emperor's son, and the son of the most powerful Tsaeci politician in the Empire, Versidue-Shaie, savvy name huh?
It was the same Tsaeci politician who allowed the assassination of Reman III, (note, allowed, not caused) and who became the first Tsaeci to rule the Empire (of Tamriel.)