Is it possible to burn things in a halogen atmosphere?
They certainly can. Put some water in the bottom of a beaker, fill the beaker with chlorine gas, and drop in bits of calcium carbide. The carbide will produce bubbles of acetylene, which will spontaneously burst into flame when they hit the chlorine.

Flame colors depend on many things, even in oxygen. In general, flames in a chlorine atmosphere will probably look slightly more greenish than flames in air or oxygen, simply because the gas itself is green. Fluorine isn't as strongly colored, and flames from combustion in fluorine will be VERY VERY BRIGHT.