Much to debate here and I've got to get to work soon, but I'll start with this:
"Rabbi Yehuda HaLevi knew that the king of the Khazars wanted to convert all his people to Judaism, which is forbidden, and wanted to prevent it. Mass conversions are not welcome in Judaism becuase there is no chance that all people in such group sincerely believe that Judaism is the truth. They either seek some benefit or they are forced to do so, such motives make the conversion phony and invalid. Khazars didn't truly convert to Judaism, they didn't become Jews."
Your argument is based upon an incorrect context. R. Yehudha haLlewi never spoke to the king of the Khazars and he probably never even visited Khazaria. He was simply using the story as a background to present his own opinions about Torah and Jews. You may DISAGREE with him on this, but it makes no sense to claim that what he writes was directed at Khazars. It was written in Arabic, which the Khazars did not understand. The wikipedia article gets it right:
http://en.wikipedia.org/wiki/KuzariAs for Ribbi 'Aqiva, what I wrote is not just something I picked out of thin air; it's based on what Hazal said. I'll have to look up the source(s) for you; I don't have it here in front of me. Of course, his status as the son of gerim had no impact on his authority in Torah.