NuMathWiki is a wiki site for mathematicians. It is a part of the numath.com website.
Everyone.
No. You can view and edit pages without creating an account. If you do create an account, your edits will be associated with your account, and you will have access to your own private namespace where you can create wiki pages with configurable permissions. Those pages are by default private, which means only you can access them, and you can grant other registered users of your choice access to view and/or edit them.
Content created on private pages by registered users is fully owned and controlled by the page's creator, i.e., it is not subject to any license.
Content created on public pages is automatically licensed under the license.
Both NuMathWiki and ProofWiki are wiki sites about mathematics. However, while ProofWiki has the specific goal of collecting proofs, NuMathWiki allows any content related to mathematics and mathematics research. See the question about allowable content for more specific details. Also, ProofWiki does not support private pages.
MathOverflow is a question and answer site about mathematics at the research level, allowing users to post questions and others to answer them, with a voting mechanism to signal the quality of answers. There are rules governing what sorts of questions can be asked. Some content that would be considered off-content would be welcome at NuMathWiki.
NuMathWiki is a wiki site, allowing users to collaboratively create and edit articles about topics in mathematics. The format is not optimized for a question-and-answer format.
Any content that is about mathematics at the research level. Some examples include: