It's unlikely to be well-received
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 :
- How they might have gotten a specific injury?
- This is about a character's backstory : There are almost always multiple, perfectly acceptable reasons to have one injury, with some crazy stories behind it which depends always on the story narrator and sometimes the character, too. Therefore choosing one is up to one's discretion.
- What might have lead them to have a certain type of personality?
- An individual can have a wide array of equally valid (read opinion-based) events leading to any behavior. For instance, I almost got drown once, it's still memory-anchored but I don't fear swimming either (even though I'm lawfully awful at it 🐘). Others in the same situation might develop long-lasting traumas however. Or just laugh at it, I don't know; it's their own personal adventure!
Extending the initial topic just a bit
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.