Is it possible for twins to be born but only one of them to have autism?

Sure. Especially fraternal twins (but even identical) can different neurodevelopmental outcomes depending on intrauterine and postnatal factors such as ischemia, infections, accidents, toxic exposures, genetic variation.
Complex issue. Autism is in the eye of the beholder. Children with genetic and developmental disorders can have autistic features. Normal children can show autistic behaviors in specific situations. Autistic behavior may develop following brain damage from infection, trauma, drug toxicity, effects of cancer, etc. Autistic behavior may develop from severe emotional stress.
Yes. I've seen it in practice.Some of the newer data suggests the cause may have already effected the egg prior to conception, so fraternal twins can be as different as other siblings, including one with autism.