Do you think my pets are happy?

I think that in general your pets are happy! You should try to convince your mom to take them to the vet though, because without health there is no happiness! You could try to find out what your pets like to do best, such as certain areas they like to be pet and things like that. As for the hamster, turtles, and hermit , they seem to be happy by themselves and there isn't much more you can do to improve their happiness. For your dog you can dedicate yourself to training him, because every dog is trainable! Maybe you could play with some cat toys for your cat, because they love toys no matter what age. Good luck!