Can tonsil stones form after tonsils and adenoids are removed? Wife has severe halitosis, great dental hygiene, non smoker, non drinker...

No. But anything is possible. Could be from GERD, gum infection, pet nasal drip, infected sinus, abscessed tooth, change in Meds or supplements, impacted food debris, etc. Start with a dental examination. Ask Dentist about tongue scraper. Let him/her do oral hygiene evaluation. If cause is not a Dental her Dentist will refer her to appropriate Physician to continue investigation.
Unlikely. In the majority of cases, the cause of bad breath or halitosis, is the product of bacteria in the mouth. Bad breath can be very embarrassing, but it is a common condition and there are numerous ways to treat it. See your dentist for Halimeter test, diagnosis and bad breath treatment that depends on its cause. Good luck.
Halitosis. Bad breath can also be caused by acid reflux, your diet, poor oral hygiene habits, cavities, and periodontal disease just to name a few. Brushing your teeth well may not do the trick. Have your dentist give you a thorough examination with a full set of radiographs and a thorough hygiene visit to rule out any dental problems. If none, consult with your physician about possible other causes.