What does her crate look like?
Does she get high value treats when she's in there?
A dog should feel completely safe in their crate, and they should actually look forward to it.
My puppy gets peanut butter kongs, bones, and chew toys when he goes in his kennel, and at this point he's actually quite happy to go in there on his own. It's also in a nice dark and cool room so he's comfortable.
I highly doubt that she has
true separation anxiety at this age. She's too young to understand you leaving and then to associate that with something bad. She's probably just lonely and bored, and crying usually indicates that she's not happy in her crate, not that she's having a panic attack.
- training (she’s not food motivated)
I've had those puppies

Try lots of different treats. Some puppies have a sweet tooth, others really need an aromatic and rare treat for training.
My current puppy would do tricks for a piece of cardboard

If she's not hungry, she may not want the treat. Try timing your training before meals.
Some puppies just want to play, so finding engaging methods and exciting toys can be hugely helpful.
Not an uncommon issue with puppies. And it's one of the things I hate the most.
When she puts her mouth on your hand, rather than squealing or swatting, push your fingers into her mouth, not hard, but enough to make her gag you out, then give her something to put that mouth on. Keeping a nylon bone, or squeaky ball in your pocket will be handy. Always tell her "No" when she's done something wrong, and always give her a "Yes" and let her know you're SO EXCITED when she's done something right, this way she'll understand that she should respect your boundaries while also not feeling frustrated.