What is the best test with the least radiation to see if the bone near #1 tooth cracked during the wisdom tooth extraction due to lousy oral surgeons?

Dental X ray: Dental xrays have very little radiation. Especially if they are digital.

Digital x-rays: Digital x-rays use an extremely low dosage of x-ray and are very detailed. Teeth and bone breaking during removal of any tooth, and especially wisdom teeth, is common and most often not because of "lousy oral surgeons"'.

Your dentist: Your dentist should be the one to make that call. If you don't trust him/her, go to a specialist (oral surgeon) and they'll help you out. Sometimes just a visual inspection is all they need. The extreme is a cbct or "cat scan".

CBCT: A cone beam 3-d image would be a good option for diagnosing a crack in any surrounding bone. The bone is this area is often very thin and soft. It has nothing to do with a surgeon being 'lousy' or not.

Cone Beam CT: If your wisdom tooth was impacted, removal of bone may have been required, which some people may refer to a the bone being "cracked". Some erupted wisdom teeth may have very large wide spread roots with extremely thin bone over the roots that can be attached to the roots when the tooth is removed. Some bone loss with the tooth removal does not necessarily mean your surgeon was bad.