That said, talking about copyright in the same context as someone "stealing" a mathematical idea shows a fundamental misunderstanding. Copyright has very little relevance to academic plagiarism: the idea of legal enforcement of a copyright on a mathematical text seems pretty unfeasible. Instead, plagiarism is punished by the opprobrium of one's peers, and whether your ideas are published with copyright, some form of "copyleft", or in the public domain, the same ethical standards apply independently of the legal situation.
]]>In terms of "copyright" (as stated in your question title): the answer is either note safe at all or completely safe depending on your interpretation. As discussed in the FAQ, by posting on MathOverflow you agree to license what you wrote under a CC license, which means that anyone can legally copy and republish what is written, provided he gives proper attribution.
In terms of "academic priority", it is generally understood that MO is a public forum with publically available, periodically updated database dumps. So it would be very foolish indeed for someone to plagiarize what you wrote on MO.
In terms of "open problems": again, this is addressed in the FAQ. MO is not the right place to post open problems. But if you do post one, and someone else solves it before you do, you probably have only yourself to blame if it is something you are working on.