Can a spayed dog be shown in the Veterans class?

Yes, they can.

Provided the Veteran class is not eligible for BOB

Can a non champion be shown in Veterans class.?

Not if the veteran is eligible for best of breed.

Yes - veterans don't necessarily have to be champions.

The spayed/neutered veterans are included in judging for BOB per the AKC rules for dog shows:
"Neutered dogs and spayed bitches would be
allowed to compete in Veterans Classes only at independent
specialties and/or those all-breed shows
which do not offer any competitive classes beyond
Best of Breed."

Thank you Linda - I was just getting ready to post that. I remember very well the thrill of seeing Ch. Chocorua's Seabreeze winning the 1992 (I believe) national specialty as a veteran. I think she was 12 at the time, and definitely spayed. Even at that age, her topline was rock solid. Seeing Ivy and Norman together for one last hurrah was an experience I and others that were there won't ever forget. I apologize for getting a little off topic....