Hello from JustAnswer.
Yes, a knee problem can cause a problem with the hip, Any problem in the knee or elsewhere in the leg that alters the mechanics of using the leg can place extra strain on the hip, and over time, this can cause hip problems.
Yes, a torn cartilage can be present and not diagnosed by plain x-rays of the knee. In fact, torn cartilages will usually not be detected by plain x-rays. An MRi is the study that will usually detect a torn cartilage. We do not perform an MRI on every person that has knee pain, but if there is suspicion that a torn cartilage is present, either because of the history and physical examination or persistence of symptoms, then an MRI would be appropriate.
As for whether there can be nerve damage from someone falling on your knee, the answer is yes, but it is not very likely. A minor nerve injury, such as a bruise would be more common. But a significant nerve injury that causes sustained symptoms would be very unusual when the only injury is someone falling into the knee. If there clearly are nerve symptoms present, it would be more likely that the trauma has caused a musculoskeletal injury that has also has some associated inflammation, and the underlying musculoskeletal problem is causing swelling that is pressing on the nerve.
At this point, it would be reasonable to consider an MRI for evaluation of ongoing significant symptoms, although the findings on exam would also guide decision making on whether to obtain an MRI.
If I can provide any additional information, please let me know.