11 Week Old Crate Anxiety

My fiance and I just adopted an 11 week old Alaskan Husky. We take her out about 4-5 times a day in our backyard for about 20 minutes each (10 mins of training). She runs around plenty and she responds well to commands, however we ran into a few issues that's driving my fiance a bit crazy.

1. The crate anxiety. We have two crates: one in the master bedroom so the pup can sleep with us within eyesight and the other is in the living room for when we want to chill out and watch TV. After taking her out, we take her to her crate and she completely goes crazy for about 5-10 minutes before chilling out. I'm not sure if it's because we're giving her very little exercise, but she seems to always whine when she goes back into her crate. For context, we do have a cat and we've let them sniff each other's things for a few days and even seen each other in person a few times now. I just don't want to let my pup roam around the house and destroy things or chase the cat around. Our cat seems to be curious/calm around our pup now though, so maybe we're just overthinking it and should let our pup roam free?

2. Our pup only seems to nip at my fiance. We both have similar putting routines with her but our pup seems to be especially nippy with her for some reason. I get that the nipping is a phase that will eventually phase out but we've tried addressing the issue so it doesn't evolve into something worse. The things we've tried include: yelling loudly, redirecting her with treats/toys, grabbing her upper jaw so she nips her lips, or just even bopping her nose. Nothing seems to be working. Any advice?