Can a broken rib cause a collapsed lung? I fell and broke a rib. Am I in danger of getting a collapsed lung?

Yes. Rare but it can happen with really bad breaks from severe trauma. Mostly -- no.
Yes, . Yes, rib fractures can result in a pneumothorax, or collapsed lung. People who fall and break their ribs typically develop multiple rib fractures, rather than just a single rib. The jagged edges of the fractured ribs can disrupt the lining of the lungs (pleura) and can.