Nostalrius Begins - Quality wow vanilla realm (1.12)

So I heard some pets know extra skills by default like claw, bite, etc and that overtime you could 'learn' this skill from the pet. Does this mean you can teach this skill to other pets? And if so do you need to learn all the levels of the skill or can you just purchase rank upgrades from the trainer once you've unlocked the first level?

Here's a link to all the pet skills and which beasts have them: http://wow.gamona.de/forum/threads/pet-skills.73897/

When you tame a pet with a skill you will eventually learn it just by having the pet use the skill. After learning it, you can teach it to other pets as long as they're a species that can learn it (a bat can't learn Claw for example). You only get the rank of the skill which your newly tamed pet has, but you don't need the lower ranks to learn it.