Yes, you can. Olive oil will affect the flavor of the muffins, so would be most successful in savory muffins - corn, cheese or spicy muffins with sage and thyme, or chopped onion and celery. For sweet muffins, I recommend canola oil because it has a neutral taste. But olive oil works for sweet muffins, too. It's used in several types of Italian cakes.
no
Coconut oil
Some of the oil can be replaced by applesauce, but not all of it.
nope
Yes, Carrot muffins are healthy. Healthy carrot muffins made with whole wheat flour, coconut oil and maple syrup. These muffins make a great, quick breakfast.
I have never seen a peach cake mix, however, a good idea is to take a white cake mix, substitute part (if not all) the liquid (not the oil though) with peach juice from canned peaches and dice the peaches into the cake. A make your own peach cake.
Yes. Oil having lesser density than juice, will float on it.
Juice is much denser than oil. Juice will sink and some what combine with water while oil floats on top of water.
Applesauce is a good substitute for oil and butter, in baked goods. I've used it many times. I've never heard of using it as a substitute for eggs. However, you could probably get away with substituting egg whites for whole eggs.
No, you can't juice things with oil in them, it can ruin the juicer
"Dont make muffins buy them they taste better bought idk why but they just do my favorite muffins are the choco chocolate chip ones they are so good especially when you eat them with chocolate milk. I know what your thinking im crazy about chocolate and yes its true!" - That is not a frickin' answer. They didn't ask for your opinion or your life story.