Rabies shots are actually determined by state or county laws. Sometimes when your dog is little the vet may delay when the rabies shot is given or may give only a half shot.

Be careful not to bathe your puppies too often; you can dry out their skin or cause skin allegeries to products.

Rabies Shots are mandatory usually after 6 months old and recommended after 12 weeks old if traveling or going outside. If the puppy is small most vets in our area recommend the delay on the shot to at least 20 weeks, but will administer if the owner wants it or if the puppy is over 12 weeks and will be traveling.
I never heard of "half-shot" being a legal procedure, since rabies is regulated and mandatory i would look into it carefully to make sure it is a safe procedure that actually fulfill the requirement of the law.
Puppies can be bathed since 6 weeks old, as needed, no more often than every 10 days and attention should be given to make sure there are no drafty breeze, the mild hair dryer is used to dry the puppy completely and avoid "coughs and colds" due to puppy lowering their body temperature. Special attention needs to be taken to make sure no water gets into their ear canal and proper ear cleaning procedure is followed.
Dry skin can be a inherited condition or can be afflicted by too many baths too often, harsh shampoos and chemicals, hot dryer, etc... It is wise to bathe as needed, keep puppies inside until all vaccinations are done, avoid unnecessary baths.
XOXO

Not too late to teach them it hurts
 

If your puppy is biting you, yell "OUCH!" to get their attention and it should stop them. They learn to play without hurting each other so you need to tell them when it hurts. I swear by it because I have used that technique with 6 puppies over the years. It always works. The idea is to sound like a litter mate or, even better, the Mama, and cry out. My dogs would learn to bite playfully, not biting down hard after this technique.