If a professor analyzed my work, does the university own my idea? If I had completed work on a certain idea, and would like to have it analyzed from an expert in the field. And shared it with a few professors, to get their opinions on my work... would that mean the university has contributed to my work? And somewhat has rights to the idea? Knowing that I never used the university's resources or facilities during the development of this concept.

I wont publish anything, just need an opinion on my work, if it has errors and overall worth pursuing.
This is a good question for the legal department at your university. At the university where I teach, there is a standard software license agreement form that I sign with students to basically ensure that software is owned by everyone at the end of the class. But your university will likely have its own rules and policies. If you have your own attorney, you can work with the university to modify such agreements.