An issue you have is she is an active breed and a working breed and she is shut in an apartment. Husky's tend to enjoy company of other dogs and to be free to run around. They are also known for escaping from yards and wandering, as that is their nature. Being in an apartment most of the day is unlikely to make her happy. I also live in an apartment and researched breeds for months before deciding on a greyhound. They are one of the laziest dogs around, they need 20 minutes of exercise and then they want to lie down.
I'm not saying you should get a greyhound, I saying this is going to be an issue in understanding Penny's demeanour and emotional state. She's stressed.
She was good the first week, it was a novelty and a new home and there would have been more attention given to her. This is perfectly natural and usual when bringing home a new pet. She wouldn't have missed the outdoors so much, but as she's settled into a routine, she will start to miss running around and possibly feel a little stir crazy being camped in an apartment.
Her enthusiasm and perceived disobedience on the leash, trying to (and occasionally) breaking free is symptomatic of her need to run and work. She's excited and fresh. Plus she's still a puppy and will be until she's 2-3 years old and completely settled. so there's that extra exuberance and need for play.
This also leads to chewing. All dogs in the puppy phase will chew and they will chew anything that feels good on their gums. The onus is on the owners to dog proof the home from teething gums. A job easier said than done. She will need plenty of items to chew on, in fact a variety, particularly when being left alone. Boredom will make her want to chew more, as she will not be distracted from annoying gums.
Whether she came from a loving home and was lost, there's likely to have been at least on painful experience with a person for her to be so terrified of you. It sounds like she is also biting out of fear. The fact she has bitten you more than once is serious, a husky is not a small dog and she can inflict quite a bit of damage.
There's something about your demeanour when your alone that frightens her. We all have different faces when others are around. Try and note you body language when you're approaching her when you're alone and compare it to when you're in company.
Try videoing yourself when you're alone and ask your partner to watch it.
A solution - building a relationship from the ground up
I would recommend trying to get her to approach you. If she is looking terrified, so not approach her. Sit down. Preferably take a step back and sit down. Tell her in a low calm voice that it's ok. Put your hands out in front of you palm down as you say this. Let her know she's safe.
You'll need to start training to overcome this fear from the ground up. Back to basics. Rewarding her for small gains. This is most difficult if you are the primary carer for the dog. If there's any chance your partner can help take over, so when you are alone with the dog, you can just sit with her. Offer her a food titbit, toss it on the ground away from you near her and praise her for taking it. With the goal that eventually she will take it from your hand.
2. In company
When others are around do the same exercises with her and reward her. So when you come into the room, you can sit and then ask her to come. Give her a titbit and praise her. Tell her how good she is and lots of pats. Not on top of her hear, under the sides of her face. So she doesn't feel you are trying to dominate her, it will be non threatening and supportive.
If she comes and takes a titbit from you in company repeat as above with the praise. It's important to put both vocal and physical praise at the same time as giving the food reward, so later any of these are viewed as pleasurable and will be rewards within themselves the dog will seek.
Another thing is to try and approach from a low physical stance. So crouching. You could even try lying on the floor when you're alone with her and see how she responds. Make your body language as less threatening as possible.
One thing is, throughout all this, patience is key.
It's important you maintain her walks, it would be preferable if you are able to put her on a leash while someone else is in the apartment. If possible avoid having to approach and handle her on your own, as this will interfere with the process of trust and safety that you are trying to build. I understand that this might not be possible.
Also speak to the shelter, and check local husky groups, for any possible guidance. If you are able to meet with other owners of the breed for play dates and some guidance it will help you.
I am concerned about this situation. Both for you and Penny. She is at a point where she has bitten you and depending on the laws this may make re-homing her difficult, which would be sad indeed. She deserves a chance, she's not a bad dog, we need to work out ways to improve her security levels with her. If you are unable to resolve this, then the best thing would be to (again) approach the shelter or some husky groups and see if there is someone who already has a husky who would be happy to take on a special case. I've found the best way to get help with any breed of any animal (especially dogs) is to approach enthusiasts of that breed. I have never recommended re-homing here before, but when there is aggression that involves biting, it is something that needs to be brought to the table.
Best of luck, please let us know how you get on.