Certainly I think that requiring research-backed answers is appropriate and welcome; if someone is asking for research we should endeavor to provide such. We're a bit more "opiniony" than most sites, and that means a lot of our answers tend to be personal narratives and opinion; we should enable users who want facts to get those when needed.
Scope-narrowing restrictions are also fine in my book. If someone asks a question, they should be able to tailor what they're asking reasonably tightly; as long as that is still a good question by itself, it's fine to me. Asking a question about a controversial topic, or simply something where people will likely have opinions or information about the wider topic area, you may often want to clarify in advance that you only want to know about a specific subset of the area - for example, asking about behavior but clarifying your parenting style so you don't get suggestions to do something that you wouldn't agree with doing. As long as the question with the restriction is still answerable and otherwise on-topic it seems fine to me - it's just further clarification.
Enforcing a specific number of things in an answer isn't really something we'd generally be okay with, and you'll notice the date on that first question; that wouldn't be on-topic currently I don't think.
Other kinds of restrictions, other than those that limit the scope or require research, should be less common, and are probably less likely to be acceptable in my opinion. As Erica points out, limiting to the point of unanswerability would be a problem, as would including the answer in the question (ie, suggesting a scope narrowing device such that the answer was present in that narrowing).