Do brain cells go through some kind of cell division, like mitosis?

Certain specialized cells like hepatic (liver) cells or neurons (brain/nerve) cells don't divide. They encounter a phase in the cell cycle known as G0 or G-not. They do not continue to divide, and this poses problems in modern medicine as some scientists work to cure paralysis; because the damaged nerve cells do not regenerate, there is no known way to cure paralysis.