What are some natural exercises/remedies I can do or take to improve my eyesight without medical treatment?

Not many. Think of the eye as a video camera with very few moving parts. Eyesight problems are usually associated with the lens system of the eye and no exercises or remedies can change their shape (just like moving a video camera around will not change the lens' shape). The only remedy for eyesight problems is glasses, contacts, or vision correction procedures. See an eye doctor to learn more.
None really. Just using your eyes to get through the day is a very active, neurologically intense process that cannot really be accentuated with "eye exercises". What you do in the course of reading, driving a car, avoiding the bus that almost ran you over, seems to be far more demanding a task than following a moving target on a computer screen in a contrived eye exercise test. No scientific support exists.