IGN : Shadowtony
Answer 1 : Starting from generation 6, Azelf has 14 while the other two have 15.
Answer 2 : There's a rumor they represent the pieces of the Triforce, Azelf being power (Din), Uxie wisdom (Nayru), and Mesprit courage (Farore).
I just did that part yesterday and I had no problem. Are you sure you're checking all of them? For me, Eevee was in the top right corner in the room where you first see it getting put into the machines (B3F I think it is). I also remember someone saying that if you lost to Giovanni the first time, you just need to talk to the police guy that gives you the quest and he'll have the Eevee instead.