For the biting:
When she nips, not only yelp but also get up and turn your back on her and ignore her. If she'll continue tugging on your clothes you may need to figure out a different way to get away from her. When Tucker was a puppy and he'd nip we'd stand on the couch so he couldn't get to us. You could also step out of room over a gate so she can't keep biting but you can still keep an eye on her. Once she calms down reengage with her using a toy. As long as she's biting at the toy keep playing, but as soon as she bites you, yelp, stop playing, and ignore her again. If she refuses to use the toys and insists on biting you it might be time for her to spend some alone time in a crate or playpen to calm down. Make sure there are toys and chewies in there for her.
It may also be helpful to train her to go pick up a toy on command or when you point to it. That way when you see her starting to get rambunctious you can remind her to put something in her mouth so that you'll play with her.
Make sure she actually likes the toys you have! Every dog is different with what they want to play with. Also make sure you know how to play and engage her with the toys. Simply holding a toy out or tossing it on the floor is not likely to attract her, really wiggle it around on ground and tease her a little (as long as she's not skittish) to grab her attention. She needs a reason to go for that rather than for people, and people are really fun because they tend to push at her and move away quickly which is fun for a dog.
I'm not much help for the crying when alone. I think most people just ignore the pup and eventually she will adjust. You can provide edible chews as long as she won't eat the whole thing or choke on any of it or put stuffed toys like Kongs filled with food (frozen will last longer). Sometimes adding some sort of white noise (leaving a radio or TV on) can help. Other people may have more suggestions, I never really got Tucker to the point where he was comfortable being alone in a crate.