No. No, that would be one of those "medical myths." eyeballs grow, and the shape of the eyeball can change through the growing years.
No. Eyes grow as your baby grows, just like his/her other organs. In addition the iris, the colored part of the eye, likely will change color during the first year. Most babies are born with blue eyes, but watch closely as your baby's eyes get more color and depth to them!
No. They do grow slower than most other organs.
No. Eyeballs grow in diameter a very small amount each year during childhood, until they reach the adult diameter of 1 inch.
No. Eyes grow from birth through the teen years.