Check out Petopia for more details and it should be on any hunters lists of good sites .
At the moment you can only have 2 permanent pets unless you have all skills and level 70 , the third slot is so you can tame pets with better skills to retrain your original pair of pets ( things like bite and claw go by level of mobs and need training new pets ) , which when the expansion comes will not be needed ( pets get their skills already unlike now ) so we will have 3 real pets if wanted.
At the moment you have to level the pet unless it is the same level as you ( it just means you killing green or above mobs ) exp from quests does not count , their health ect. is linked with yours and also with their level , if you read up here you will see many threads about levelling pets. When the expansion comes out it will be easier as if a pet is more than 5 levels below you it will close that gap to only 5 levels , which at 70 will probably still take ages to do.
Stable slots First is free , Second is 5G third is the pet you have out so max of 5g , and then it is all free to change, i have not heard/seen ? about any changes in the expansion for stable slot prices yet .
I suggest you read up at Petopia for more details and here as you treat hunters pets a lot different to what you have been used to , for example if your first pet is a cat it may or may not come with Claw and Bite , you have to tame a beast that has those skills and learn from it so you can train your pet , and as you level you have to find other beasts with a higher skill you want to learn and go tame them , when the expansion comes at least we will not have to do that any more as all pets will already know the skills .
I hope this comes close to answering your questions.