Hi. I new and I have a few questions.

Where do I go if I want to buy a pet from another player but I don't want to go through a their hatcheries or stables? And how can I earn diamonds? I can't buy them at this. Would facebook credits work?

You can buy diamonds from the diamond shop. Sometimes, festivals are hosted (like the Week of Love Festival going on until the 19th of February), which there are contests (official games and contestssection in forums) in which you can earn prizes, like diamonds. You can catch pets while battling from pet traps but I don't recommend it. Some people will have very cheap pets in their stables and hatchery, but I really don't know how to answer the first question. I hope this helped! Also, if you want any pets in my hatchery, you can pick any! I'll set them up for you to buy, 1 gold if you want!

You can use the advanced search (top left corner) to search for pets to buy. You can choose the species, gender, traits, and price range. That will give all the pets that is on public sale that fits your requirements.

You can get diamonds either by spending real money and buying them from the diamond shop, or from saving up gold, and buying them from other players on the trade broker. Otherwise, sometimes diamonds are given out as prizes in official and unofficial forum games.

You'll need to use paypal to buy the diamonds, so no, facebook credits won't work.

OK thank you. I'll give it a try. And Tickley123 thank you for the offer^-^. I would like to see them :)

Alright head to my hatchery and take a look! Any of them you want! (Except for the sylestis in the first page from slots 17-21 and 25, and the second page of pets are also not for sale. If you want, I could breed two of my sylestis together and give their egg to you! Here's the link:
https://www.sylestia.com/view/hatchery/?userid=46645