Before you read what I say, please read this meta post: What's the official SE response to serious mentions of suicide or self-harm in posts?
Go back, I'm serious. Read it.
First case, at-risk user.
If you ever find a question where you believe that the asker is at-risk, either from harming someone else or themselves, then you must take the following steps exactly:
Close vote. No upvotes, no downvotes, no answers. Close vote the question as off-topic.
Flag for a moderator's attention. That question needs to be locked/deleted immediately. We don't want anybody to answer the question, or start talking about it, or voting on it. When you flag for a moderator's attention, be sure to give a quick insight into the situation. From here, the moderator will take the appropriate actions, and will escalate the situation to the community team.
Optional: Add a comment. If you wish, you can add a comment. You want to show empathy, and provide directions for resources. Here's a sample, stolen from the above Meta post:
It sounds like you’re going through a hard time. I’d really like to help you, but unfortunately, we’re not well equipped to do so here. Your best option is probably to call a suicide hotline. People are on call there to talk to people struggling with the same kind of issues you are, regardless of location. If calling is not good, you can chat with them live online. It might not help, but what’s the harm?
In cases like these, the community team will then reach out to the user, and handle the situation from there, often by making sure that the user is alright, that they are being heard, and that they get the support that they need.
Here's another case: those "self-help" questions.
Now look, you folks aren't professionals, and you shouldn't be expected to act like one. You don't want to be diagnosing anyone with anything, nor do you really want to be addressing any particulars of a diagnosis. If somebody tells you that their arm is broken in a chatroom on the internet, you shouldn't tell them how to make a sling, you should tell them to call an ambulance!
If you find any question that appears to be asking for any kind of medical advice, I would recommend that you close it as off-topic with a custom reason. This helps track it in our stats (to see if it's a long-term issue), and also allows you to explain why we have to close the question, mitigating any arguments from the question.
Last case: Casual discussions about mental well-being.
You should basically treat the question as any other. Depression is a fairly common diagnosis, and is heavily stigmatized. In fact, the World Health Organization said that 1 in 4 people will be affected by some sort of mental disorder (again, read it!). That doesn't mean we should send it away, but it's something that in many cases, there is no harm in talking about. As long as it isn't close-worthy for one of the two reasons above, and that it isn't attracting any unhealthy discussion, then there is no harm in keeping it around.
Find a question where you believe someone may be at harm? Close it, flag it, find a moderator and alert us to it.
Find a question where you feel the asker is seeking medical advice? Close it with a custom reason, and probably a good idea to let someone know.
Find a question where there's a healthy, casual discussion about mental well-being? Well, nothing much to worry about there then!
Since you linked three examples, I figured I would classify them under the above three cases, and maybe add a brief comment:
How can I explain my reduced social activity when depression is stigmatised? I'd say it falls under Case 3. You can tell that curiousdanii left a comment making sure that the user is aware of support systems - which is good.
How to talk to a dean about depression? Another Case 3. Good communication question. The well-being aspect is not central to the question. Nothing to worry about here.
What to do if I/Someone I know is feeling depressed/suicidal? Feels like Case 1. I've got to say, this one scares me a little bit. Depression is not the same as being suicidal, the question is trying to appeal to broad audiences, and I do not feel comfortable providing any advice of any sort. There's something that is ironic in that answer:
"While you may think that contacting family or friends is a good idea, they are not qualified, nor do they have the proper knowledge or training to offer the appropriate support in these situations."
Yes! And neither are we qualified either! We should be getting them to someone that can provide them with advice - and we are not that someone. Suggesting that this question should be a duplicate target is ridiculous - we need to follow the Case 1 steps above, and handle this on a case-by-case basis.