Is a tonsillectomy considered major surgery?

Yes and no. Surgery should never be taken lightly. Any surgery that you have is major. Having said that, tonsillectomy is an operation that carries very low risk of serious complications.
Not usually. Most tonsillectomies done in children are relatively quick procedures. There can be, though, major complications like bleeding and airway obstruction. Tonsillectomy in adults can be more involved if they are done to treat obstructive sleep apnea or cancer. In patients with osa or morbid obesity, you may be required to stay overnight to ensure your ability to breathe through post-op swelling.
All surgery w/risk. Any surgery can have complications, and should only be undergone if necessary. Tonsillectomy in adults is extremely painful.