How long will a sinus CT scan take? It's faster than an mri, right?

CT is faster.. Once you are positioned on the table, the actual ct scan takes only seconds to perform. It is much faster than mri.
It depends but quick. The length of a sinus ct depends on the machine doing the test, but they're generally very quick, particularly if it's a "spiral ct". It may only take a minute or so, not including the setup and discharge. An MRI takes much longer, but may show more soft tissue changes which may be important to your doctor. Which test is ordered depends on the pathology present and what they're looking for.