LOL - you've got several problems here, Sean.
Yes - the sugar (white granulated, powdered/confectioners, brown) DOES
make a difference. Yes - the fat (oil vs shortning) DOES
make a difference. Unless you understand the CHEMISTRY of baking and how each ingredient works with the others ... you have only three choices: (1) Follow the recipe exactly, (2) Find another recipe that uses the ingredients you want to use that is formulated for those ingredients, or (3) expect a lot of failures.
And, the method of cooking also makes a difference. Generally (and I don't know of any exceptions to these terms): GRILLING - the heat is close to, or directly applied to, the food from the bottom, BROILING - similar to grilling, but the heat is applied a short distance (usually 2-6, but can be as much as 12 inches) from the top, BAKING - heat is applied from the top, bottom, and sides. MICROWAVING works differently - the heat is generated by the water molecules being excited (they basically vibrate) and that causes heat to be generated from the friction of their movement ... so food basically cooks from the inside out (that's just a 5-cent description).
Here is one example ... solid fats have a higher melting point than liquid oils (which are already liquid) = the higher melting point of solid fats allows the dough to "set" before the fat melts ... so the cookies do not spread as much. Altering the sugar(s) affects the browning and crispness/tenderness.
You may want to try one of these recipes:
Oil cookie recipes
Microwave cookie recipes
Hope this gives you a workable solution.
Oh, by the way - what brand and model of grill/microwave do you have? If we had an idea of what you are cooking with we might be able to give you some better answers not only here but in some of the other threads you have started.