All that behavior is perfectly normal for a puppy his age. The best thing for a puppy is routine...when you are training make sure you ALWAYS have treats on you to use as a reward. Keep training sessions 2 - 3 minutes tops. Their attention span will not keep him focused on you longer than that. Try to make everything positive with him to help build his confidence. To get my puppy to follow me on a leash I always had treats (hotdogs cut up) on hand to encourage him to want to be with me. Now he does on his own. They are very smart dogs if you can stick to a routine he'll pick it up fast! You've only had him 7 days...you're still new to him. Let him get use to his new environment. There's nothing wrong with you're puppy...don't demand so much of him, he's a baby. He will never make you happy if you expect a perfect pup that doesn't bite...they all do at that age. German Shepherds are called land sharks : ) For our pupppy, we redirected him when he was biting something he shouldn't....everyone always had a toy on hand...he learned fast what was acceptable to chew on. Good Luck!
Isen Vom Kavallerie - DDR/Czech GSD (pup in training)
Red - Rescue GSD (CGC)
Gypsy - Yellow Lab (CGC)
At the Bridge....Charlie - GSD (2014) and Shiloh - Lab (2010)