Can sacroiliitis or bursitis cause hip to lock?

Not usually. Depends on what you mean by locking. In can be from an internal hip problem (like a labral tear or osteoarthritis) or from an external hip problem like "snapping hip syndrome" or something completely different depending on what you mean by "hip locking" . Sacroilitis usually causes very focal pain over the sacroiliac joint and can sometimes cause radiation into the buttocks, groin, hip, or leg.
Not usually. Sacroilitis is usually posterioly in your buttocks. If you feel locking or catching in your groin it could be a labral tear of your hip. I hope thus helps.