Is there any way to mass feed foods to my pets? Or do I have to do them one by one? Thanks in advance.

other than the resort in veta lake and the in in omen islands nope its 1 at a time

If you want to feed individual foods (like for the gourmand achievement) then nope, you have to go one at a time. You can use the Veta Lake Resort or Omen Islands Rathskeller Inn like said to keep your pets full and happy, but there's also no penalty for not feeding or playing with them. They won't be able to battle if they're hungry, but nothing else will happen to them

Thanks for answering my question, both of you.