At what age degeneration of the brain starts and by which test one can know more about it?

That depends on what kind of degeneration you are interested in. From age 9 to about age 20 a person can be taught to read much faster than normal by expanding the field of vision. For a demonstration, try looking at two words instead of one. That alone will double your reading speed. If you are still young it is possible to read an entire line or even more than one line in a single glance. The memory expands at the same time to retain what you are reading. After age 20 or so it is no longer possible to teach a person to do that. Once learned, the ability remains until middle age, degrading slowly from age 40 or so to age 60 or so.

One mark of a genius is that he does all his most important work during his teen years. The only exceptions were Ramanujan, still going at age 32, and Euler, still going well into his 60s.

There are some conditions associated with age, but almost nothing is known for sure about them, especially what age they are associated with.