Why does some cookie recipes both put sugar and brown sugar? Also can we use sweetener like stevia instead of sugar in recipes?
You are asking a surprisingly lot of questions.

First, to deal with this question, you need to understand "creaming".

So look here and here.

Nothing "creams" as dramatically as granulated sugar with room temperature butter. Those particular ingredients are special for that. Brown sugar doesn't accomplish nearly the creaming effect of granulated sugar, but combined with granulated sugar the combination is greater than the sum of its parts. In other words, a 50/50 mix of brown and granulated sugar can achieve nearly the leavening effect of granulated sugar only with room temperature butter.

The sweetness of brown and regular sugar are pretty much equal. In the US and I think almost everywhere else, brown sugar is just granulated sugar with molasses added. Brown sugar adds the molasses flavor, and not surprisingly, some browning.

To use non-sugar sweeteners, choose recipes that don't call for The Creaming Method, they simply won't work right. If you want to use a sweetener other than sugar, pick a recipe with a fat that is unsaturated (liquid at room temperature), or melted butter. Also, be sure that your sweetener of choice will maintain its sweetness if baked.