Yes there is a specified rating but I don't remember exactly what it is. I know it was good, I got the same answer from all my navy/seal buddies.
I'm sure the song is comical but I can't click the link and I'm too lazy to type it in.
Statistically there is a very low probability of passing buds, but there is no way in hell I'm washing out. The nice thing about the navy is that if you fail buds you still don't go back to the main fleet, you can opt to go to a buds academy of sorts where they train you for a second try at it (lol).
As for the ASVAB I don't do well on written tests, and I see no reason not to study for it and score the best that I can.