German Shepherds are not the easiest dog to train IMO. They thrive on human interaction and alot of them will also stick their finger up at you when you tell them to do something, they are very good at sensing anxiousness and under confidence.
7 months is still very young, it can take dogs weeks, months to years to fully settle in to a family and the environment. You need to keep doing the basics, taking out after eating, drinking, sleeping and playing, this will reinforce the behaviour you are asking her to do. She may well be toileting in the crate because of stress, then eating it can be a coping mechanism. How long is she crated for and when? Have you properly introduced the crate? Look for signs when in the house such as sniffing, ,scratching, circling etc, these can be indications she needs the toilet. I know you have said you have done everything but if she is performing this behaviour then you havent unfortunately, it just takes more training and time with some. If she toilets, dont have eye contact with her, ignore her, remove her from the room and clean up, then let back in and again ignore. Do not tell off for the behaviour.
Quite alot of dogs do eat their faeces, i wouldnt worry too much, keep her on lead when your taking to toilet and after she has toileted reward and walk her away, if she turns to the toilet then just say a firm no and walk away. Just make sure you are not accidently rewarding her for doing it, some people do and dont realise. Talking in the wrong tone of voice and facial expressions can sometimes come across as rewarding for the dog.
With regards to the hyperactivity, she is still a puppy IMO, she is going to be hyper, most GSD'S are. As others have said, the food can make a huge difference, wagg and pedigree and not the best and will cause hyperactivity. Mine are currently on dodson and horrell, its not that expensive and is a very good food. Try and look at some other brands, it will help her alot. How much exercise does she actually get ? do you play games in the garden and when out such as ball games, frisbees, training like sit, paw, down spin etc ? She needs to do some brain work activities, it will make her focus and is actually very good exercise and stimulation. With the pulling on lead, i would get a gencon, mine have gencons and it means i can have full control and they can not pull. They can now walk on slip leads most of the time as they will not pull. Also you i would look for a trainer as you can then do some work on loose lead training. Dont go out if she is hyper and pulling, make sure she is calm and listening before the lead goes on, otherwise she doesnt go untill calm.Also you can try scatter feeding, it gets their minds working and provides exercise, either in the house or garden.
You need to get her listening to you, if you let her get away with somethng then she will not listen anymore. Get a whistle aswell, i feel it helps reinforce bonds, blow the whistle, treat and keep repeating just in house, then as soon as you blow the whistle she will be there waiting for treat and next instruction.