Hello! I was wondering if outside trading is allowed? (Selling Sylestia animals for things on other websites?)

It is, but you have to make pms or posts about the trade as "proof" that you are not multiaccounting. also you need to verify if the other game also permits cross trading

I have seen cross-site trading here before. The admins here doesn't stop it, but if you do it, it's at your own discretion, since they can't really do anything if your deal don't go well. =/

I believe cross-site trading falls under Term IV A in the terms of service
IV. Transactions
A. We allow the real life goods trading of currency for Site assets, such as pets, items, or currency. However, this is done at the player's own discretion. Please use the appropriate forum and take great care while doing these types of transactions. All transactions involving the Site's assets must be done on Site with another Site player. Although the Site and its Staff takes no responsibility or liability for transactions between players, any players found to be scamming will have their account terminated and receive a permanent IP ban.

So long as you're not breaking any rules on the other side, this site permits it, but if anything happens with your deal, the admins won't be able to help you.