First, any time an option is greyed out, you should hover the mouse over it. The game will tell you why it's not selectable.
When taking screenshots for the cooking guide I had no trouble cooking all dishes (except hot dogs) indoors. My Sim at the time was using the very best stove available, which may have a grill component to it.
All dishes in the game can be cooked (for a price), without having the ingredients on hand except for ambrosia and baked angel food cake, which both require rare ingredients.
This thread reminds me. Someone said that actually shopping for the ingredients at the store is better because your Sim will buy nice ingredients, rather than the default, which seems to be normal. Something I want to test to be sure.