1) vets: Dr. David @ Creature Comforts makes home visits and is a fantastic vet
Dr. Mike at Pets Central in Sai Kung is also fantastic
2) dog hotels/kennels:
kennels: Ferndale has a good reputation, as does Pet World in Yuen Long
Boarding services: my husband and i run a home boarding service for dogs (DB DOG DAYZ), where your dog lives with us and our other "boarders" in our home
Hotel: Dogotel in mongkok, only thing i know about it is that it is incredibly expensive
3) if your dog is well trained, you can take it to the country park and let it off leash...but please make sure that it is well trained.
4) we've only used a groomer to shave one of our dog's thick coat, once per year. we do it the rest of the time, so i can't tell you who is "good" or not.... sorry