Can you get tonsillitis if you have had your tonsils removed?

No. However, you can still get infections of the throat. It's really pharyngitis not tonsillitis since the tonsils are (or in your case, were) part of the pharynx.
No. Tonsillitis is inflammation of the tonsils with a number of possible causes. Without tonsils, this can not happen, unless the surgery did not remove everything.