Welcome to pet battles
Having rares will add advantage, but you still have to learn the tricks to defeating your opponents. Check out the some of the awesome guides that this site offers for pet battling http://www.warcraftpets.com/wow-pet-battles/
As for the upgrade stones on AH, i personally wouldn't bother wasting the gold unless you have it waste, during the many pet battles you do, you may be lucky to loot one at the end of a battle. Additional once you start unlock the various dailies, the stones have a chance of being in you reward sack.
I personally haven't used the FFF and Onyxian whelpling much, but i think you may have a difficult time using just the two. With the right combinations you will be able to use two max level pets to level a third pet. Keep in mind tho, some of the NPC trainers can be a nightmare, what works today may totally bomb for you the next day. (that could be just in my own experiences tho)
For your last question, I'm going to go out on a limb and say no........ it may be possible but I really do think that possibilty would only come after many many many battles and you don't sound like you would like to spend the time doing that
FYI my "team" consisted (at the start) of 15 different pets, I still find now that they aren't all perfect but having a good pool of alternatives does make battles a lot easier.
Hope I've answered your questions, Happy Hunting