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.
This answer touches on the problem:
Superfine sugar will dissolve too quickly and won't allow enough air to be incorporated.
Powdered or superfine sugar will still give you the same sweetness property as the granulated sugar. However, the step of creaming butter and (granulated) sugar is not just for mixing. It also incorporates some air into the fat; a well-creamed mixture will look "fluffy" and paler in color.
In creaming the butter and sugar together, you are using the sugar to
aerate the butter and fill it with bubbles that can capture the gasses
released by your leavener. The more fine bubbles you have in your
network, the lighter in texture your cakes will be and the finer the
crumb. This is true for your muffins as well, while it makes your
cookies light and crisp instead of hard and dense. (King Arthur Flour blog)
Best Answer
Sugar is not really a wet ingredient, it's just treated as one in certain types of baking (i.e. cakes).
When making a cake or other "fluffy" baked good, you want a fairly small amount of gluten to be produced, otherwise you'll get a chewy texture instead, and you definitely don't want a cake to be chewy like bread.
Dissolving sugar in the water inhibits the gluten-forming proteins. It's a method (actually, the method) of adding more liquid to the mix without getting a tough, chewy cake. It is for this reason that sugar is considered a "wet ingredient" - because the process only works properly if you add it with the water, not with the other dry ingredients.
It's even possible for sugar to be a dry and wet ingredient in the same recipe; you might add just enough sugar to the water to get the right texture, and add more to the dry ingredients for further sweetening.