Personally, I am of the opinion that Doshu Morteru Ueshiba is the head figure of Aikikai. Yes, there are various shihan and instructors with variations, and that is fine. BUT... given the question was directed toward Aikikai, I'm surprised no one mentioned "Best Aikido: The Fundementals" and "Best Aikido 2: The Aikido Master Course" both written or co-written by Doshu.
These books don't necesscarily go into kyu grading requirements, as every organization is different. However, these books explain and illistrate aikido techniques in a very excellent way and are very through.
As far as requirements for the Aikikai go, the closest thing I can find is this table of requirments here:
Your instructors may have something different. Always refer to them. I do like to learn as much as possible to be as prepared as I can be for any test. That last link... if you are ready for those requirements, you should be good to go. But again, always consult your sensei. It will be He/She who is testing you when it all boils down to the end.
PS: The books are really great!