May other professional researchers ask questions at MO?
Yes, they can, and they do.
However, questions have to be stated clearly and in a way which is understandable to mathematicians. Keep in mind that the audience of the site are mathematicians.
It is mainly the job of the person asking the question
to state the question clearly and rigorously in the language of mathematicians.
How do they decide whether their questions are at research level?
Researchers in that area can tell if it is a research level question or not, and
often other mathematicians can also.
It is more difficult for people who have much less knowledge about the area of the question, the first thing to try to answer the question by themselves, Google, check Wikipedia, check undergraduate textbooks, etc.
Demonstrating your own effort to answer the question
result in a much more positive feedback.
In practice being a research level question
is not as strict as it might seem at the first sight.
E.g. a researcher in one area of mathematics
while working on a problem
may face a question from another area of mathematics.
The question might be quite easy for an expert in that area
but not the original researcher.
That can be a fine question.
A question doesn't need to be difficult or on the edge of the mathematical research
to be considered research level.
What is really expected is that the question is related to research,
the author of the question has tried the obvious things to answer it,
the question is well written and interesting to others and
is not trivial to answer
(e.g. something that almost all mathematicians should know or
a good undergraduate student who have taken a course on the topic can answer).
- you have good reasons to believe that a mathematician can answer the question and
that the expertise of a mathematician is required to answer it,
- you have spent time to write a clear question in the language of mathematicians,
- you have written a brief motivation section explaining why you are interested in the question,
- you have demonstrated that you have done your own research and
have tried to answer your question yourself first,
then it is much more likely that your question will get positive feedback on MO
even if it is not strictly speaking a research level question,
it will just get migrated to MSE if it is really off-topic for MO.
Also keep in mind that there are several other sites
where the question might be more suitable:
Mathematics, Physics, PhysicsOverflow, Computational Sciences, Theoretical Computer Science, Computer Science, Cross Validated, ...