I think you did right, due to the dog acting up. If the dog had acted normally I would have given a 20% which would have been $6. If it is the owner of the grooming shop and not an employee of another, I might give only $4 or $5.
I think you did right by tipping $10 due to your dogs...
No, dogs are pack animals and want to be with their pack (you). So sad for this puppy. Why did you get it in the first place? If you are already tired of it and just plan to stick it outside then find it a better home. I hate to see dogs neglected. A dog is not an animal who is solitary...
Yes, you should neuter him. He may be excited because there is a female in heat somewhere in the neighborhood. The dog is probably bored and lonely. Bring him inside and make him a part of your family. Dogs left outside are not properly bonded with their people, because as you say, you don't...