I have 6 pets, and I am wondering how I can feed them all??

You can stick them in the resort in veta or the Inn in port plunder and it will keep their hunger and happiness at 10/10

Do they still work while they are in there? And can I still use them? Ex: for training??

Yup you can still train them and stuff in there. You just can't feed them food items or play with them with toys

Thank you!! :D