A.A.
I have lived with German Shepherds (GSD) my whole life, I own two of them and I am a dog behaviorist.
There are several issues here. She is WAY too youg to be separated from her litter mates and a little too young to be weaned. Puppies are weaned at 6 weeks by their mother and need to stay with the litter until they are 8 weeks old at least. She may have started eating solids when offered so the breeder may have felt she was old enough to send home to another family. However I really question the breeder qualifications if they didn't know they should keep the puppy with the mother until it's 6 weeks and with the litter until it's 8 weeks.
She is NOT teething right now. Puppies go through a teething stage at around 4-5 months of age. True teething lasts about a month when they are losing their puppy teeth and getting their adult teeth in. During that time they have a NEED to relieve the pain in their mouths to chew on things very similar to human children. Any chewing that happens after that is for boredom, association, or to relieve stress. Any chewing that happens before that is usually a puppy learning about life as most dogs learn by "touching" with their mouths not with their paws (hands), or boredom.
GSD's are a very "mouthy" breed. So what that means is they like to keep things in their mouths. This is a breed that is well known for walking up to their owner and greeting them by gently putting the owners' hand in their mouths. As puppies it is a VERY common behavioral problem to want to nip and mouth on any exposed flesh. There are several things I could recommend that you do, but with the other issue's that you've listed I think it's best that you consult as dog behaviorist as soon as possible to have someone show you how to get a handle on this behavior.
Puppies at that age should NEVER NEVER NEVER show aggression. Is she really growling or is she playing with you? GSD's can be a very vocal breed expressing play with some growl like noises, barking, "talking", wimpering, whining, etc. If she is truely showing aggression, you need to take her back to the breeder and either get your money back (I would recommend this cause is sounds to me like poor breeding) or get a new puppy that is a better fit for your home.
What kind of food are you feeding her? You don't really need to get puppy formula, however you should consult your veterinarian as to what kind of nutrition she needs at this point. Most likely she needs her food softened by soaking it in a little chicken broth before feeding her.
Is this your first dog? Your first GSD? This is a breed that can be very challenging to own and if you do NOT have experience with them I STRONGLY encourage you to seek out a trainer or behaviorist to help you learn more about the breed, and how to prevent unwanted behaviors. Most trainers that offer group classes will NOT be able to accept you until she is 4 months old and been fully vaccinated, so I think you should look for a private behaviorist that can get started with you as soon as possible. I do NOT recommend waiting until she is 4 months old to get her into a group class.
Please feel free to email me if you have more questions.
A.