I have a 16 yo high functioning autistic son, so I have a few ideas. You also posted about problems feeding him... so first, young kids can be picky and autistic kids are pickier. It sounds like you are doing as much as you can. At this age, you probably won't be able to reason with him much. I couldn't with my son.
If he gets upset, you can try taking a light blanket, wrapping him up in it and holding him firmly and rocking him. That worked well for my son. Sometimes these kids get overwhelmed with all the stimulus (too much sound, light, touching etc) in their environment and need a way to block it out.
When my son was about 5, we started him on a gluten-free, casien-free diet and found that was very helpful with some of his behavior problems. It also seemed to help him focus better at school. There was a segment on Dr Oz just a few days ago where that was mentioned. It's not 100% guaranteed to work, but often helps these kids. It won't hurt him and could help him so you have nothing to lose there.
He should be in the pre-k program 2-3 days at your local school since he is 3. The program my son was in was wonderful. He is in high school now and in regular ed classes. He's not an A student, but he is doing OK. Don't give up hope. Your grandson can have a very good life and be a productive member of society.
Hope this helps.