Like @
Greycloud said, the nipping/mouthing is just for attention...any attention will do. So the smacking etc is rewarding for Spectar. I would go even further than Judy though and say that when teeth touch skin or clothing you don't just ignore the behavior you actually get up and leave the room. Completely remove yourself from his space. Go into a bathroom or bedroom and close the door and wait 30 seconds or so or until he settles down...as in isn't howling or jumping or barking. Only give him attention (good, bad or passive) when he is being relatively calm. Which, in his case right now, will probably mean more like "not completely out of control."
You'll be exhausted because you'll be up and down 100s of times a day. You'll sit down and he'll nip, you'll get up, leave and wait. You'll re-enter the room, he'll nip and the cycle will repeat. Rinse and repeat. Eventually though he will get the message that when he nips all the fun stops and the behavior will disappear. The key is consistency, everyone
has to do it and do it
every single time. When Freya was a pup I swear I spent months on end in and out of the bathroom teaching her that it was never okay to nip.
If he is only responding to commands 50% of the time then he
doesn't know the command. Go back to the beginning and reward faithfully for the behaviors. Dogs don't generalize well so if he knows sit in the kitchen, he very well might not know it in the living room, out on a walk or at the pet store. Look up Kikopup on YouTube. She has tons of free videos that will help teach all sorts of useful manners and behaviors.
Generally speaking dogs aren't willfully disobedient or bad. They do things because they don't know any better, not out of spite. They will do whatever behavior because it gets them what they want. If there is no reward for that behavior they will stop doing it, plain and simple. So, you say he's potty trained, but then poops in the crate. Start rewarding and praising him for going outside and he will stop pooping in the crate because it is not rewarding. Don't punish him for misbehavior because that "punishment" is
actually rewarding...especially if he comes from an abusive background. NILIF is about only giving him rewards (in his case you will get far simply with attention because pit mixes are so people oriented) when he doing what you want. So don't pet him unless he's calm, don't give him his food bowl until he is sitting nicely, don't give him a treat until he has sat. He doesn't go out into the yard until he is sitting nicely by the door. The leash isn't put on until he sits. Every single little bit of interaction is not done on your part until he has exhibited a positive behavior (whether that is actually sitting or simply the absence of something negative...like being calm instead of jumping, barking and nipping).
Also, dogs do not "attack out of the blue" or "start to turn". In almost every single case there were plenty of warnings that people ignored...sometimes blatantly and others times simply because they don't know. I can't tell you how many videos I've watched on YouTube where a dog is throwing calming signals left and right, clearly showing that what was happening to them was making them uncomfortable and the people around are giggling and clueless. I often wonder if years down the road the dog is finally fed up that it's been trying to communicate its discomfort and no one has been listening, so eventually it will bite. Dogs can't tell you that what is happening makes them uncomfortable, they try to show you with their body language, but when that fails they use their teeth. For some dogs their threshold is so far out there that they might never bite...for others their threshold is very, very low and they will bite from just a little discomfort.
To get something away from your dog that you don't want him to have start to play trading games. Where you take something away, but give something back. You start this with stuff that you don't mind him having and you're showing him that you're not stealing what he's got and that he'll be getting something good in return. Eventually he'll be gladly giving up even the most yummy thing because he knows that other yummy stuff will be coming his way. Watch out, though, sometimes they get so good at the game that they find stuff to bring you knowing that you'll trade them for something else!
Lastly, like many others have said he needs exercise, but he's only 9 months old it is a really bad idea to run him hard on paved surfaces at this age. His joints are still growing and that sort of exercise can do really serious damage in the longterm. Instead exercise him in spurts on softer surfaces until he's at least 18 months old. Your instincts were right and a dog park is not a good option for a young, exuberant, under stimulated pitmix and would just be asking for trouble. Instead, look up a flirtpole. It's great exercise when space is limited. It needs to be played with in a controlled manner, which means your dog needs to sit and wait, drop, leave etc and when done correctly it teaches your dog self-control in no time flat. It's cheap to make and there are no shortage of instructions available online. If your area has a fenced baseball field those are often great big spaces where you can exercise your dog off leash without fear of him running away or strange dogs interacting with him. Just be sure to pick up after yourself and in most cases nobody minds. If you can find somebody with a well socialized dog who has a similar play style and let them play together (while supervised of course) that is another way to drain some of his energy.