No he was not, IIRC. You may be thinking of the prophecy that says "Dragon-Born" but not "Dragonborn". I believe those are two different things or something the devs left in the abyss of the fandom.
That depends on lore interpretation.
Seeing how Nerevar fit the usual Dragonborn persona's (ambitious extraordinary hero kings) not to mention that Nerevearine practically fought against Lorkhan/Shor (both Tribunal and Dagoth Ur in this case represent him as they use his powers), as fits a child of Akatosh, I am going for the Dragonborn theory. The priests said themselves that they were not sure what it means IIRC. Seeing as Dunmer would not know much about Dragonborn lore, it would be surprising if they said anything else.
But that is topic for another forum.
Either way, Dragonborn is not protector of the Skaal. Not only are they Nords of a different culture than the Skyrim Nords, Skyrim said to Dark Elves: "We support you in stealing their lands!" so a Hero of Skyrim has a good reason to side with the Dark Elves, even more if he himself is one.