After injury, take rest at least 2 weeks afterpain relief. Then only use any kind of method to loose weight.

    If the injury is recent better to rest and let the injury heal on itself(or get operated for it if required), depending on your injury.     Once the injury has healed a stationary cycle or elliptical is a good option for rehabilitation,cardiovascular exercise and weight loss.

Static cycling is good for the treatment of knee injury patients when recommended by a ortho surgeon. For weight reduction, i recommend yoga based exercises.

Stationary cycle or elliptical is any day better than treadmill as your knee range is controlled and in fix manner as long as your feet position is fine. But on a treadmill it’s super variable and can cause more injury to knee and ankle , especially the jumping while running on it can cause impaction injury which is avoided in cycle or elliptical

It depends on the type of knee injury, duration since the injury, whether or not any procedure is performed for the injury and current healing status of the injury.

"any kind of knee injury" is a blanket statement and the blanket answer would be to avoid it and go for something like swimming which is far superior in terms of fat loss and also safer for the hips and knees.

Which knee injury?