My mother had a little boy yorkie several years ago, and he was terribly food aggressive and possessive just like you described your dog. He was so unpredictable and frightening. Mom had gotten him at about three and a half months old, and it got to the point that I didn't allow my children to be around him at all. "I" didn't even want to be around him. My mom went to the vet, hired a private trainer who swore he could help any dog... Well, after the trainer saw one episode of snarling, lunging, etc, he was shocked and eventually my mom had to rehome the Pup at about a year and a half old. It was sad. My mom has since wondered if dogs can have mental illness just like humans!
Most dogs can be loved and trained into good behavior. I'm just putting my two cents in
that sometimes you can do everything right and not get any results.