Puppies do start losing their teeth around 4 months of age, and they will continue to lose them up until around 6 months old. You may or may not notice they are losing teeth, as many of the teeth get accidentally swallowed. Look in the carpet, their water bowl, and check their toys for tiny teeth
The back molars, which they lose after their tiny front teeth, are easier to find. You will notice your puppy chewing on EVERYTHING during this time. One of Milli's favorite teething toys was an old sock, stuffed with a couple ice cubes, and then knotted just above the ice to keep it inside.
You don't HAVE to shave their ears, but as Sookie said, it will help the ears to stand when they're puppies, and many people prefer this as it looks neater.
3 months seems a bit young to take them to the groomer, however, you will want to start taking them to the groomer around 4-5 months for small things-like a bath, a nail trim, or an ear shave. That way, they can get familiar with the new place, the person doing the grooming, and with the process. Right now, touch your dog all over-hold each nail, brush teeth, hold up the tail and ears, etc just to get them used to people touching all of those places. Your vet and groomer will thank you, because it will make their jobs much easier.