Can I use raw sugar to make cookies instead of granulated?
Granulated sugar is 100% sucrose with the molasses removed. Raw sugar on the other hand is refined sucrose with its natural molasses. The answer is yes, you can use them but you might need a bit of tweaking within the recipe. If your raw sugar looks a bit more like brown sugar then your chocolate chip cookies would come out more chewy (not that its a bad thing) because of the molasses in them, whereas granulated sugar would yield a crumb that is more crisp. 

P.S. Its alright to use powdered sugar. Some recipes even call for it when baking cookies. However, when substituting granulated sugar to powdered sugar, i recommend that you use a scale since powdered sugar holds so much air when packing into a cup measurement. Measure 7 oz of powdered sugar per 1 cup of granulated sugar.