Do the pets ever get any other skill than blow, rush etc...? Having a dumb moment on the third skill even though i just had a battle lol.

Or is there a way to obtain other skills or abilities?

I know Simurghs can be bred to inherit "Song of Peace".

Once per island exploration, if you a have a Simurgh that knows "Song of Peace", you can click the "Song" button in the action command list to send the enemy beast away peacefully.

You won't gain experience from it, but it is helpful when you encounter a tough beast and want the battle encounter to end immediately without running away.

"Song of Peace" will not work on Beast Temple opponents.

Yeah, the Song of Peace is the only exception I think. There won't be another skill besides bite, blow, or rush, but pets with certain genes may end up with a "special attack" when they use one of these skills. For example, 

Lykos with the Ice Breath gene: Replaces Bite attack and increases its damage by 50%. 

Roc with Steel Beak and Electric Gland genes: Required for Lightning Strike. When combined with Electric Gland, replaces Bite attack and increases its damage by 50%

Cockatrice with Poisonous Claws: Your pet's claws are covered with poison. When using Blow or Rush, there is a 50% chance to poison your opponent.

Also, genes (Sharp teeth, Ice Spikes, Sharp Feathers, etc) can augment the attack strength by increasing blow/rush/bite damage by 15%/30%/45%. 

ok thanks is there a guide on this at all?

Complete gene library here: https://beastkeeper.com/gen-lib

I found this guide that explains how genes affect battle stats: https://beastkeeper.com/thread/3382