I'm not sure about the purple part. I think it's just what her insides look like, but I'm not a vet. It's my understanding it's safe to use honey almost everywhere.
The prolapsed vent can be gently cleaned with warm soap and water, gently dried, and coated with honey. The honey will lubricate, protect, soothe, and act as germ killer. After lubricated with honey, gently push the prolapsed back into the vent with a lubricated finger. Keep inside in sick bay...