University Test Bank Website- Potential Liability Issues?
Of course, we don't know what your university's academic dishonesty rules say.  But in most cases they are pretty broad, and there is probably a clause that could be interpreted to include your website, if your university's authorities decide to do so.  I think the odds are good that there will be at least one professor who is upset enough to push them to do something about it.  They might just try to get you to take the site down, they might try something harsher.  There's no way to know.

In general, I think most professors are aware that students may be informally sharing their exams with one another.  For that reason, they usually change exams from term to term, and if they reuse questions, do so only after several years.  However, some may be startled to see it done as systematically as you propose, and try to stop it.

I am not a lawyer, nor do I know your local laws, but posting an exam on your website would probably violate the copyright of the professor who wrote it (unless you have his or her permission).  This would be another avenue someone could pursue if they wanted your website gone.

Finally, professors could try to prevent their students from posting their exams on your website.  For example, they might stop letting students keep their graded exams.  Or, they could add a line to their syllabus that "you may not share your graded exams with anyone", on penalty of failing the course or academic dishonesty sanctions.  This could not only deprive your website of material, but also make it so that students can't even share their exams informally anymore, which I assume is contrary to your goals.