i can explain, when a pet gets to lvl 50, once he eats, if it has not a skill, the pet will learn a "completely random" skill, the skill can be forgotten by using the "forget" option on the pet, for what i know, the food does affect the kind of ability it can learn, only the high graded foods gives the best abilities, like pet food, fancy pet food, the rare drops from mobs and drops from high lvl bosses, this have a bigger probability of learning a better skill.
also, you can't expect a mob pet to learn the "all round" skill, the strongest skills are for "boss pets" and "god pets" (non of these pets have been released)
the "mob pets" and "event pets" learn from the same list of skills, some of the best for this are
homming (improved hit rate), evasion (agi+10), self healing (self recovery +100%), dual blow (attacks twice instantly, very useful for the low aspd classes like some gladis and samurais) and sonic boom (magic attack, power increased by distance)
all this skill i had learned, so i can explain them
the strongest skills are only for boss and god pets
scape, all round, quick turn, spell boost, hide attack, high cycle, life charge, large shield, i dont know what this skills do, so i cant explain em because the pets have not been released (i read from other post that someone was trying to know what escape skill does, but i guess he was just curious, not because he had it)