* Were teachers in this time period less aware of warning signs of potential suicide? Neil literally tells Keating “I’m trapped” which is a massive red alert considering the situation and Neil’s emotional state.
** Look how many times people commit suicide out of seemingly nowhere these days, even with increased mental health awareness.
** Keating also does seem reluctant to meddle in his students' personal lives. He stops the boys from going after him and the father when the play is over, telling them they'll make it worse. So maybe he did see some signs but told himself he shouldn't interfere. Neil did at first tell him that his father came round, and while Keating obviously suspected he was lying, didn't get confirmation until that night - which is the same night Neil kills himself anyway.
** The short answer is "yes", but it's worth pointing out that it's not just the time period, it's also the kind of place and people we're dealing with. Schools like Welton were (and are) primarily reserved for those who come from some kind of privilege - even if the current parental generation isn't particularly wealthy, there would likely have been wealth and status a few generations prior - and who tend to have their lives mapped out by their parents from the moment they're born. That then breeds a mentality in outside observers that they've got nothing to be suicidal about (since they're financially reasonably well off and set for life in terms of prospects). Ironically, Keating is probably even more susceptible to this since he's already gone through Welton's learning environment himself and was probably a lot like Neil at the time he did which, even if his conversations with Neil raised any kind of alarm bells, would likely cause him to think "I went through it and came out alright, so will he". Suicide among teenagers struggling with huge amounts of parental and societal pressure was certainly a thing that occurred but it wouldn't be talked about, empathised with or analysed in the way it is today with an emphasis on finding out exactly what their mental state was or even knowing what the signs are; more likely the whole thing would be swept under the carpet and dealt with as quickly as possible and with as little awareness drawn to it as possible to limit the "scandal" factor, both with regards to the school and the family.
** In total fairness, "I'm trapped" might also mean that Neil simply feels stifled and frustrated, not that he's seriously considering suicide. Keating's only human. If it were that easy to realise that someone was genuinely suicidal and intervene, no one would ever be able kill themselves.

* At the beginning of the movie, Neil's dad says that the principal thinks Neil is taking "too many extracurriculars". Mr. Perry's solution is to order Neil to drop his favorite one, the school paper. Since ''none'' of Neil's extracurriculars have anything to do with becoming a doctor, and since Papa Perry clearly doesn't want Neil to drop ''all'' of them (after all, they look good on the college apps), why not let Neil pick the one to drop? I mean, if you're gonna micro-manage a decision ''that'' unimportant, why not just keep him at home so you can make sure he cuts his food to the right size bites? (Never mind the question of "what business does the principal have telling somebody their kid is taking 'too many extracurriculars' in the first place?" Real-life principals '''LOVE''' kids who can do all that and still keep their grades up like Neil did.)
** The problem might b that Welton isn't exactly about real education. It seems to be a training center for future leaders and power-holders. Typically, schools like that tend to cut out any education that detracts away from power-and-money-seeking, such as drama education that might expose students to what it's like to live in other people's shoes, or to freely express themselves. It wasn't ''really'' about Neil taking too many extracurricular activities, it is about the specific activity Neil chose. The money-and-power hierarchy has to sustain itself somehow, and the best way to do that is to give almost unlimited authority to power-holders, so that the students will further commit themselves to a life of endless competition for the top. How to make that prize attractive so they'll submit to all this competition and stress "for the greater good?" You make the prize attractive by giving the students a firsthand taste of what powerful people are allowed to get away with. It's like when a father is allowed to repeatedly abuse his son, and then when his son grows up he acts like that towards his ''own'' son because that way he can finally exercise power in his life.
*** In that case, why does Welton even ''have'' a student newspaper?
*** It has not been unheard of for future leaders and power-holders to own and operate newspapers. What better way to teach them the importance of controlling information than to give them experience in how to control it? Mr. Perry simply happened to disapprove of his son working in that area.
** The short answer is that Mr. Perry is clearly a ControlFreak who might not have objected too much to the other extracurriculars but clearly didn't approve of his son working on the newspaper for whatever reason, and so ordered him to drop that one.
** Also, Neil was a straight-A student. If you take too many extracurriculars, there's a possibility you devote less time to studying. In the 1950s, the attitude toward extracurriculars was different than it is now.
** College admissions are irrelevant, everyone attending that school was from the class where Ivy League admissions are guaranteed from birth.
*** Except for the Perrys, which was the point. Mr. Perry can't really afford to send Neil to this school, but he chooses to anyway because he truly believes it will put him ahead of his social class.
** The principal note above: no, they don't, or at least not always. This troper attended a performing arts school, which is literally run on extracurricular activities, and it was not at all uncommon for administrators to get bent out of shape over students participating in them, regardless of grades and other academic performance. The obsession with "distractions" is still very present and very damaging.
** It's not that "none of the extra-cirriculars have anything to do with becoming a doctor." A deleted scene clarifies what else Neil was involved in and they'd all contribute to becoming a doctor/part of wealthy society in ways the annual doesn't: Chemistry club & mathematics club (both important subjects for medical school), Welton Society Candidates (a prime social-climbing opportunity), and soccer (all the boys have to do one sport). So yeah, basically Neil isn't allowed even one, vaguely enjoyable extra-curricular that deviates from his Dad's assigned life plan.
*** It also highlights that Mr Perry is extreme even compared to other Welton parents - Charlie (future banker) is on the paper and doing two sports, Knox (future lawyer) is on the paper, Todd (brother of valedictorian) is part of the school annual. Neil's dad is just a total ControlFreak.
** RE: the principal, extracurriculars do look good for college and such, but they're "''extra''curricular"; they're basically sidelines to the main curriculum that the student needs to complete in order to have met the school's baseline requirements for graduation and / or any further legal requirements for graduation that might also apply. [[note]] Every student, regardless of their interests and career pursuits, usually needs to have earned a certain amount of credits in mathematics, the sciences, literacy etc. A governing body has often made them minimum legal requirements to determine that a student has completed an education in the subjects that society deems important and valuable. [[/note]]The time to complete extracurricular requirements has to come from somewhere; if the student focuses more on the extracurriculars, that means there's less time to focus on the main curriculum.
*** This was especially the case in the 1950s and in such a prestigious academy, where there was a lot more rigidity about what students "had" to learn to be functioning graduates. The principal is most likely bringing it up because he feels it's a possible point of concern that Neil is focussing so much on extracurricular activities he's at risk of letting his focus on the main curriculum suffer; he might be doing okay now, but the principal is pointing out that it might not stay that way. And it's his business because, well, he's the principal of the school, he's the one who's ultimately responsible for making sure as many students graduate as possible, and he's the one responsible for advising the students and their parents how they can best ensure this or if there are any potential problems with this happening.
* Did Todd sign the document? I know that he says "they made us all sign it" and the most important authority figures in his life (his dad and the principal) pressing him to sign it is pretty good incentive that he DID sign it. But on the other hand, he's the first to stand on his desk and we never see him sign it. Is there confirmation of either?
** There's not, but this is something the viewer just has to take as implicit. We see a scene of Todd, already well-established to be quite timid and easily cowed under pressure, basically being bullied and pressured into denouncing Keating, we see a scene of everyone looking glum and it being established that Keating has been fired, we see Todd unable to contain himself and yell out to Keating that everyone was forced to sign the document when Keating briefly stops into the room... the movie is basically asking the viewer to put two and two together. It's not directly shown, no, but it's all but outright stated that while Todd didn't want to, he was forced to sign the paper, and out of guilt he feels moved to reassure Keating that neither he nor the other boys were willing in denouncing him.