Israeli scientist Dr Moshe Feldenkrais developed the method in response to his knee injuries.  In the 1930's the prognosis for surgery wasn't good.
He based his system on physics, engineering principles (biomechanics), and human development - as babies we learnt through self-exploration.
Much like learning to play a musical instrument, or improving your golf have to slow down and think about what you're doing.
Lessons involve slow movement and mental attention to change your movement habits.
Many reasons, often because of pain that keeps reoccurring in spite of treatment.
Other reasons are injury prevention or rehabilitation, to improve posture, breathing, and balance, to maintain mobility with aging.
A bonus - it relaxes and reduces stress.

The lessons are experiential - you just have to do them yourself.
Depends on many factors, primarily one's willingness to learn.
You are learning how to sense yourself more clearly.   Some people have naturally good kinaesthetic sense, for others it can take time to develop.   That's when the lessons really engage your curiosity and interest.
My oldest client was 95.   She credited the Feldenkrais Method with helping her maintain good balance and remain independent.
Yes, I work one to one with teens (adult classes are too slow for them).
They learn really fast.
Yes, indeed Dr Feldenkrais became well known for helping people with these conditions.
Obviously, with physical damage to the brain, more work is required.
The method doesn't "cure", rather it helps anyone to improve function.
Absolutely, good function is essential for good performance, and injury prevention.
Dr Feldenkrais helped top US basketballer Julius Erving regain goal shooting ability after a jaw injury.
You take your unconscious habits into everything you do.   Improved body awareness helps you refine exercise technique, such as running, tennis, the gym, pilates, or yoga.