What tests should a child undergo before general anesthesia for an ear operation?

Healthy children. Don't need any tests. Your child's medical situation should guide any testing.
It depends. If the child is otherwise completely healthy, then probably no tests are necessary. If there are any co-existing illnesses or genetic factors present, then certain lab tests or other studies may be required, depending on the situation. If you are concerned, consider yourself entitled to request a pre-operative anesthetic consultation with an anesthesiologist, they should be happy to oblige.
Talk to MD. There are no required tests. Your anesthesiologist will decide what pre-operative labs and tests are needed based upon examination and history. Sometimes this interview is done ahead of time, so that you can ask the doctor questions about the care of your child. I hope all goes well.