Is it appropriate to ask a question based on a bunch of other History SE questions?
In general, yes.
However, in addition to citing the questions from History:SE that inspired your question, you should also document your preliminary research in the body of your question.
So, to continue with your example of medieval widgetbricks, a brief, and non-exhaustive, checklist might be:
Is there a Wikipedia page about widgetbricks? If so, what does it say about medieval widgetbricks? Why doesn't that answer your question?
Check to see if someone has already posted a question on History:SE about the particular details of medieval widgetbricks you are interested in. If there are other questions about medieval widgetbricks (beside the ones you've already cited as inspiration), make a point of explaining why they don't answer your question. This can help avoid having your question wrongly closed as a duplicate.
Carry out a Google search for
medieval widgetbrick, and any other keywords you think might help (other search engines are available). As a general guide, start broad with as few terms as possible, and add additional terms to narrow the results as you go. Include the details of your search(es), the search engine, and the results returned, in your question. Even negative results help others not to have to duplicate that research. What more are you hoping for? (Be as specific as possible.)
(Remember that other people may receive different results for the same search, depending on their location and past search history (among other factors), so don't just assume they can reproduce your search results).
You should probably also search for keywords on Google Scholar. Include the details of your search (for example
medieval widgetbrick), and the results returned, in the body of your question (even if it's just saying something like "nothing on the first few pages of results looks like it might contain the answer"). What more are you looking for? (Again, it helps to be as specific as possible).
If you do find interesting books / papers that look like they may answer your question, but they are behind a paywall, then list them in the body of your question. Someone here might have access.
Put those same keywords into the search box on Internet Archive. Do any of the books or papers returned help? Even if they didn't, you should at least say why you think they don't help in the body of your question, so that others don't have to repeat your research.
- Even if your research does eventually answer your question, you might still consider posting a self-answered question if you feel that the answers you found might be of interest to others. This can be a great way to document your research.