Hello again,
A big thanks to all of you for your replies!
I've considered everything you've written, and since I last wrote I've both been talking to my boyfriend, and tried different approaches to see what works best with Penny.
After telling my boyfriend that I had written in these forums to get advice, and then told him what you all said (I skipped the parts about him needing psychological help though, he's already in therapy for anxiety issues so um, no need to add more pressure), and it seems like he finally understood that I hadn't just been talking rubbish because I'm too "nice" to show her who's in charge. I also told him that there's a very big difference between dogs, cats and parrots, as both dogs and cats are carnivores whereas parrots are prey animals. When I told him this it was like flicking a switch, he seemed to find this argument rational and understood that one can't approach all animals in the same way. In a dog - owner relationship a struggle can be more "fair", the dog is a carnivore and can potentially hurt a human badly, and vice versa. Note that I am not saying that it's ever okay to hit even the most fierce of carnivores, I think all human - animal relationships should be based on trust, but in cases where you and your dog get into a conflict I don't think it's super harmful to sound and look angry. With a parrot however it must be completely different, as they are prey animals. If an enormous creature (one you don't know very well yet, at that) comes toward you, growling and showing their teeth, it's probably very scary. After all, being eaten is one of the possible outcomes in the world of a prey animal.
We also agreed that whenever Penny does something we do not like, he will just leave it be and I will take care of it. This is because I'm sure that even though I'm no pro, and might not always succeed in stopping said behavior immediately, I at least have enough knowledge from previous experience to not do something that will break the trust between us and Penny. He will only do positive things, like giving treats during training and giving scritches. I'll do that too (of course) but he's not allowed to intervene if she does anything she shouldn't. If he finds something troublesome he'll tell me, and I'll take care of it. Does this sound like a reasonable solution? It was the best I could come up with for the time being, at least.
Regarding prevention, I am doing my best to keep her occupied and stimulated, and I have done so since the moment I got her. I therefore don't think this was the main problem. I tried covering our TV with a blanket though, and she lost interest in it. Now I've even taken away the blanket, but she shows no interest for the TV at all! Seems like it worked out okay

The same goes for our bookshelf, where she used to display nesting behavior. The nesting behavior in itself wasn't very troublesome, the only issue was her chewing my books (I'm studying and some of them aren't even mine, they're the library's!). I put towels in all shelves to cover the books, and it seems to work out pretty well. When she goes to try chewing on most things I've figured she's only really interested in discovering what it is, once she's figured something out it's not that interesting anymore. Therefore I took out the metal inside my old headphone cord, then gave her the cord. She chewed on it for ten seconds, then dropped it. Now she won't even touch my new headphones, I guess she had them "figured out" and has her mind set on finding new, more interesting things to chew.
I think it was Wolf who wrote about the issues with having a small home, that's exactly our case! Right now it isn't very problematic, but I've found out it sometimes makes training a little bit difficult, as there's many interesting, distracting things around. Our kitchen is the least stimulating room we have, so I've been trying to train her using a kitchen chair as a perch. She must like it, 'cause now she flies to the kitchen, perches on the chair, then starts clicking! It's really cute, and I'm glad she enjoys the clicker

She also sometimes does this right after she's eaten, so I really think it must be because it's fun and not
only because she's hungry and gets treats for it

I try to not let her go hungry, I don't like the starving methods some people use

And oh, I'm not thinking of Michael's weight/food management, I've read about that and it seems okay, I'm thinking of actually starving your bird, I've heard some people do this.
As for the screaming, it was really only something she did when she first got here and my boyfriend came home. I think I already wrote this, but in her previous home they had a dog, and both the dog and Penny would go bananas when someone rang the doorbell or entered the house, and the owners promoted this behavior as they found it amusing. What we've done since we got her is that we simply ignored her screaming (we absolutely didn't start cheering, like they did, lol) and today she's begun only chirping when someone comes home. So that's not an issue anymore, I just mentioned it as I think that was what made my boyfriend frustrated in the first place.
Actually everything seems to have gotten better since my boyfriend calmed down and realised the problem lied with him and not with neither her nor me. My guess is that Penny could feel his frustration (no shit, he was pretty obvious about it) and therefore acted worse when he was home than when I was alone with her. Now that he's calmer and working on himself and his own feelings instead, I think both him and Penny seem more happy and at peace. He's doing his best to treat her well, and luckily she seems to be a very forgiving parrot, she has given him a second chance. I don't think I can describe with words how thankful I am for this!
And indeed Pajarita, I told him the very same thing the instant he said it! It was actually kind of funny because he's really only used to dogs, and veeeeeery treat-happy dogs at that. Like, my family's dog, for instance. Give her a treat, she'll love you till the end of time. Very simple. His mom's dog is exactly the same. Luckily I think he's now also found the charm in parrots. It can be hard to earn their trust and you don't always get along, but it's all well worth the struggle in the end. I actually think this is what makes a human-animal relationship interesting and rewarding, knowing that you really had to work for it to develop. How much fun would it be if you got everything you asked for immediately? I think one would stop appreciating the satisfaction in working hard and then getting rewarded for it
