Would a non-contrast MRI show a tumor located on the skull? Are there limitations? Bony protrusion?

Depends. Depends on tumor. If there's a lot of calcium in the tumor then, contrast may not be needed to see it. If it's a meningioma then, contrast may not be necessary because of the Dural Tail sign seen on FLAIR images, however, contrast is generally given to PROVE it. But in other cases tumors may be hidden if small, no mass effect, and no contrast. Contrast always best if mass suspected.