It makes sense to talk about the core communities of each forum, so that it becomes easier to understand the scope and the differences. Not being active on the mathematics forum, I will give my belief, which hopefully matches the intent, of the community for that forum.

MathOverflow has a community of professional mathematicians employed in academia and industry, graduates and undergraduates who wish to learn at a deep level the work the professionals discuss, and other professional and nonprofessionals who are similarly inclined. This community (specifically those who are doing graduate level study) is at or near the forefront of the body of mathematical knowledge, trying to increase it. Their goal is to discuss things at this forefront. In particular, they normally don't do homework problems, unless it is closely related or extendable to their work. They also share references, so that members can educate themselves enough to get close to the forefront.

I believe mathematics.stackexchange has a wider variety of members, including many from MathOverflow. Here the focus is not on the professional frontier, but on topics and areas of wider interest. Perhaps this includes a competition problem, or a new twist on a problem regularly taught in classes. Sometimes a standard problem is discussed, to reveal a way of thinking that prevents people from seeing a solution, and how to change that to make the solution more apparent. The members here are interested in exploring mathematics at many levels, not just professional. However, solving routine homework problems or reviewing old contest problems is not part of the intent. The community is looking for new and interesting mathematical topics.

Both communities are willing to help new members if it looks like the new member will fit in and help further the forum mission and serve the interests of that community. If it looks like that won't happen, they won't devote the time. As a result, one should find a way to contribute well from the start. Most often this is to provide a good answer, but sometimes one can start with a good question.

What makes an answer or a question good? That such a post serves the community interests. For MathOverflow, this is a well written post that normally talks about a specific topic in the forefront and asks an accessible mathematics question or gives an accessible answer to such. (There are some exceptions such as big list questions, which I won't discuss here.) For the other forum, it is a well written question or answer that makes a community member feel their time was worth spending in reading and thinking about it, usually because they learn something from it.

To answer your questions, read the fora and see which posts are well received, and try to imitate those. Use the meta to vet your first or your challenging post to see if it fits community norms and will be seen as a positive contribution. You can also search meta for specifics about cross posting and other items which reveal the nature of good posts and bad.

Gerhard "Go Find The Blue Mud" Paseman, 2020.06.04.