Can brown sugar be substituted for granulated sugar in cinnamon sugar?

Brown sugar is not as sweet as white sugar. It also affects colour hence brown sugar often being used in flapjacks and with stewed fruit (speciafically apples) to make the fruit look more caramelised

you could but the results will not be the same

Yes, it can. Caster sugar is also known as "superfine" sugar, and it dissolves better when used for baking. That said, granulated sugar will still work just fine. Hope this helps!

Usually, but for texture concerns no.

No, brown sugar is less refined.