It is stated by Charlotte in Chapter 1 that Bruno is an archduke with authority above a prince. It is very well known at this point that he is a strict man who would not go along with a 'play pharmacy' that would bring disgrace to the profession. It is safe to say that he absolutely would not tolerate a member of his own family being involved in such a thing. I don't remember what Elen's court rank is but it's almost a certainty that there is no chance of her going behind Bruno's back and pressuring the Queen to let Farma run a 'play pharmacy' with the Queen's endorsement. Bruno would use his superior court rank AND pharmacist rank to overrule and possibly crush Elen for such a stunt regardless of their relation. Palle would know about court intrigue and his father's temperament so at this point you are just projecting Palle's dislike for Elen and trying to give voice to impossibilities.
Palle is definitely arrogant; referring to Chapter 21 he states that Novalute Academy is the pinnacle of the pharmacological world, that he is in the thick of it and that being there fills him with pride. Ironically he then admits that the inventor of the microscope is unknown but bizarrely continues on as is if it (or the insights it provided) is an achievement of Novalute. Also I might have found an interesting plot hole (or bad T/L) in chapter 21 where Palle refers to Farma as a 'proper pharmacist', however many chapters later when confronted with this situation he seems to have downgraded Pharma back to only being an apprentice which indicates his assessment(s) of Pharma not really being objective at all.
It's also worth noting that this is not the first occasion that Farma and Palle squared off about medicine. A prime example was Chapter 22 when Palle was trying to treat Charlotte's hiccups, he shows similar behavior when Farma flatly calls him out on terrorizing her. At that time Farma passes his treatment method off as something that was in one of Bruno's books, but most importantly he personally solidly demonstrated that Palle's knowledge is not absolute. In the current chapter though Palle angrily rejects that Farma (with Elen vouching for him) could know something he does not. The difference of course is that Palle personally put effort into determining his own condition so there is no way that someone else could know something he doesn't.
In Chapter 54 Palle asserts that he hasn't been able to identify his illness, that no doctor could, and even his father could not. However it's impossible for him to realistically assert this since he is keeping it a secret not only from doctors/pharmacists but absolutely from his father. Based on Farma's white lie Palle is already aware that their father knows things which Palle does not and are not in the Novalute text books (this is both true and false since Bruno knew more about white death than was in the text books but may not have known about treatment for hiccups), which means Palle is just making up falsehoods in his own despair. Speaking in practical terms if he had truly sought out his father's counsel, then Bruno would have gotten Farma involved and this whole interaction would have been smoother.
As for the pharmacy; Palle has already investigated it to some extent in previous home-visits, he had just never had the opportunity to visit since it's always closed when Farma had to attend to his brother. Just a mere 2 chapters ago Palle believed that the pharmacy was promising enough that he wanted to visit it because there was a possibility they might have medicine he could use to treat his condition... until it was revealed that Farma was running it at which point Palle flew off the handle. The credibility of the pharmacy itself wasn't really in question before that, but he didn't have high hopes that it knew more than he did.
I never stated that (in Palle's mind) Elen presented her case as a "play pharmacy". On the contrary, it would be more realistic to assume that she pressured the decision makers by insisting how important such a project would be to his growth and education (due to his father, there are a lot of expectations for his bright future). Bruno might be strict, but he still wants his sons to succeed and I'm not convinced he would step in if Elen were to manage to convince the court by herself - he might resent her for going over his head, but making a racket about this would be brining rather shameful attention to himself and his family, making it harder for them to gain favour on their own in the future. Once this is a done deal, the best way to deal with it is to shut up and keep an eye on things and hopefuly keep them on a short enough leash to avoid some public screw-up.
You're comparing things way out of scale. It's one thing to believe that there's some obscure method to get rid of a harmless condition that Palle just hasn't heard about, since he'd hardly be motivated to even search in earnest. It's quite another, that your own life-threatening condition, that can't be pinpointed with all the literature you can hope for, is just a matter of inexperience and not looking in the right places. For all his bluster, Palle is considered capable enough to study in Novalute and he's right - it is the best school around, even Bruno thinks so, after all. Remember, if he were unsure which illness it is, since many fit the bill, then it would be reasonable to seek his father's opinion, despite the risk of him finding out. However, that wasn't what happened. He had absolutely no idea what it could be. That kind of situation is expected for a layman, but not a soon-to-be elite specialist with access to the best sources of knowledge in the world. It's only natural to assume that it's an unknown condition, so asking his father would only alert him to the fact, that his son is dying. Note, that even if Palle knew that Bruno was better than anyone gave him credit for, he also knew he was no miracle worker. Afer all, what Bruno found out about TB would not have made a difference for the Empress or himself. He simply categorized it as an unknown illness for which there's no cure.
How do you figure one decides the credibility of an establishment, while never having been a customer or seeing it operate himself? He was intrigued, true but that's about it. He probably heard some good opinions from the citizens, but would you put your trust in just that, knowing all you do about how unreliable the medicine of this world is and then seeing the pharmacy being run by the kid you KNOW doesn't have what it takes?
I'm not saying that Palle's attitude is a great example of a scientist or doctor. He's hotheaded and pretty set in his presumtions. That's not uncommon for young people, who feel they've achieved a good measure of success. However, it's not like he's acting unreasonably, at least condidering the sum of true information that he has about the state of his brother, which is not a lot.
On a personal note, please stop assuming I'm "projecting" something here. I do not know what's in someone's head, much less a fictional character's so I'm trying to guess what a rationally thinking scholar would conclude in this situation. That's all. You on the other hand, are trying to devalue that by stating I myself am not thinking rationally, without even demonstrating that in discourse. I'm sure I don't have to tell you what that kind of fallacy is called.
