Does the worldbuilding stack accept questions relating to a single character. For example, how they might have gotten a specific injury, or what might have lead to them having a certain type of personality?
If this is the wrong ace to ask this, is there a right place?
Questions about the action of a character in a story are off topic. It doesn't matter if they have happened or they are yet to happen.
As Tortilena says: Character development is intrinsical to story writing, therefore it's unlikely such questions will be well-received, and likely to be closed for being either opinion-based, story-based or plain off-topic.
Practically speaking, this means you need to learn how to ask this vorboten sort of question in a way that doesn't violate WB.SE rules. I'm not suggesting you come up with a way to circumvent rules, but rather come up with a way to view the topic from a different direction.
As asked, and as Tortilena and L. Dutch answer, your query is one that focuses on narrative. We don't do narrative here. So, what do I mean by looking at this from a different direction? Quite simple!
How the character might have gotten a specific injury? Rather than focussing on the off topic narrative aspect, you should keep one or two skeletal narratives in mind, but ask about the world elements that come into play during those narratives. For example, in stead of focusing on the story of a woodman who injures his leg after a surprise encounter with a traveller from a different world; focus in stead on the underlying elements. Keep in mind the characters you'd like to interact while asking questions about travel between worlds, magic, technology, etc. When the answer to your question about magic or interplanetary travel comes in, you'll be able to write the narrative of how your character got the injury without asking us how they got the injury. You'll know how they got the injury because in the end, you asked us the right question the wrong way!
What might have lead to the character having a certain type of personality? Again, rather than asking us an opinion based query about picking one something from a list of somethings, keep in your mind a general arc that will answer the question you have about the character, while asking us questions about underlying principles of the world. For example, personality traits might arise from an individual's experiences, right? So rather than asking that question, keep in mind that you want to focus on experience, but ask questions about the psychology of experience and the biochemistry of the brain. Asking questions about the physical, psychological and spiritual natures of your fictional character's race will allow you to fill in the blanks. Your question about a character's personality shall be answered simply by gaining a better understanding of the mechanisms by which your character functions. Again, you'll know how they got their personality because you asked the right question in the wrong way!
No
Keep the following in mind:
Worldbuilding (on-topic) is the creation and consistent use of descriptions and rules governing a fictional world of your own creation wherein an infinite number of stories can be told.
Storybuilding (off-topic) is the application of worlbuilding rules and descriptions to a specific character, circumstance, or story.
There is a legitimate argument that the creation of the proverbial Non-Player Character (NPC) could be part of Worldbuilding. Such a character is a "fixed piece" in the world. However, we've deemed it impractical to try and identify a difference between an NPC that wouldn't make choices and is basically just window dressing for the story and a principal character that would make choices. The closer you get to an individual, the harder it is to justify backstory descriptions as Worldbuilding.
Further, there is no Storybuilding stack. It's been considered many times, but storybuilding is so far outside Stack Exchange's original intent that we're all sure it'll never get past Area 51.
Stack Exchange bills itself as a place where people can find the one and only best answer to a question. Wholly objective and wholly defined. Worldbuilding is intrinsically imaginative and we tread the boundary of Stack Exchange's guiding principles. We can exist because when one fully focuses only on worldbuilding, there really is just one best answer for their problem and that answer really is objective in nature. The problem we regularly face is that people intermix worldbuilding with storybuilding or, worse, are looking to brainstorm to avoid writer's block (storybuilding). This is why we have such a love/hate relationship with list questions. But that's another discussion for another day.
When asking questions keep in mind that the goal of the site is to help you build your world, not to tell your story.From help center
Character development is intrinsical to story writing, therefore it's unlikely such questions will be well-received, and likely to be closed for being either opinion-based, story-based or plain off-topic.
If we take your example questions :
A single character's mind is off-topic, but you still might see questions about psychology here or there. These questions can be on-topic, but the butter!
Compared to topics about physics or biology, they are really not easy to write; Both askers and answerers tend to confuse a single character's psychology and what happens on the mind of all society's members. You can tell that regularly extremely stressful situations leads more often to post-traumatic stress syndroms, but you cannot ever reasonably tell if your hero(ine) will have PTSD because of stress : a statistic about one individual is just too inaccurate, and many individual factors prevent from predicting the result at all.
Add in a general "fuzziness" in both words used and results which tends to make such kind of question unclear or feel unspecific. There's more detail about these issue here but point is, if you want to ask about the psychology of a society's component, you should slide your thumb on your keyboard 7 times to get the time to think carefully on your question. And ask in the sandbox beforehand, people should be able to tell you how to make it better if they can.
