We got her at 6 and 1/2 weeks, so she is now 8 weeks.
Anytime we play with her she goes directly for our hands, feet, leg, arm, etc. even if we have toys in our hands and are trying to distract her with the toys. She isn't breaking skin but we definitley have marks all over our bodies. At first they were not painful though they have started to get harder and harder and now she is not wanting to let go which is why I was worried about the biting.
Currently when she bites we just try to do redirection to a toy, as our puppy trainer discourages grabbing the muzzle and/or yelling no at her age.
She does well with the little training we've done at home so far. She is learning sit and come already and does those pretty well for a puppy her age.
You sound just like me a few months back when Tess, my 5 month old GSD, was the same age. She was a notorious land shark! Let me tell you, when Tess would bite, which was pretty much all of the time, she would break skin, her teeth were that sharp and still are. I was worried that Tess was an aggressive puppy and that it would continue when she grew older. Even though I had puppies in the past, none of them were as hard as she was. I tried everything but nothing worked. I would go into my bedroom, close the door and cry at times. I found this board and listened carefully to what everyone else had to say and what they were going through with their puppies....pretty much the same as me. I read back over most of the posts regarding puppy behavior and learned that GSDs need a lot of guidance and very strong leadership. I hired a trainer, put her in some daycare classes to socialize her better, and work with her every day.
As you mentioned, your pup is very smart and picks up on things easy and that's a good thing. Use that, tire her out by stimulating her mind, make her think. Work on teaching her the easy commands first, like sit and down and then go from there. Most importantly, get her in some training classes!
My girl is 5 months now and is doing so much better, she's actually a different dog now, but I had to work at it. Tess wouldn't even walk on a leash outside of our backyard, I would get her as far as the corner, if I was lucky, and she would run all the way back to the yard, pulling me behind me. Now she will walk with me all over the neighborhood, staying pretty much beside me on a loose leash. We're still working on her healing but I know she will eventually get that too.
Hang in there, you have a very normal puppy. I know it's hard when all they do is bite. I can remember mornings when I would open up her crate to let her out and she would charge right at me biting every part of me that she could reach. I had scratches and bites on my hands, arms, legs and ankles, she even bit me in the face one day. They get so excited and want to play, they are babies and they don't know any better.....yet...
Hang in there, it will get better!