Can I make powdered sugar for a cake from brown sugar?

No, you can't make powdered sugar using brown sugar. Powered sugar is dry; brown sugar is not. Cardinal rule in baking: Make sure you have ALL needed ingredients before starting. If you don't, either make something else, or go to the store.

Not to use as icing, but fine unpowdered used instead of white in a fruit cake or gingerbread

That's not how powdered sugar is made

powdered sugar is usually used for the frosting/icing not in the cake batter itself. You can use the brown sugar, a little cream and butter and cook it in a sauce pan to make a fantastic glaze frosting. this won't be fluffy, but I like less frosting/icing on my cakes.

Brown sugar is made from adding 1 tablespoon molasses per cup of white sugar!

Yes you could put the sugar in your 'grinder'/blender and grind it down, or you could use it as it is. I often make cup cakes using muscavado sugar or brown caster sugar as I think they taste nicer and are less processed than white sugar, plus they make a nicer colour of cake!

Did you know that a blender only blends food and does not remove anything from the actual food??

No you cannot make powdered sugar out of brown sugar.

If it's the only sugar you have then go ahead, although it adds its own distinctive flavour. If you also need to use it as icing sugar then blitz it in a food processor or grinder to turn the sugar grains to powder.

Brown Sugar Cupcakes makes 12 cupcakes 1 cup loosely packed brown ... But I'm like, cake-impaired or something and can't bake a whole ... Add in brown and powdered sugars gradually, with the mixture on low speed.

Brown sugar has a distinctive taste, nothing like powered sugar. I'd leave it off rather than use brown sugar.