Yes. Just search vegan cupcake recipes on google or substitute the egg portions for a bit of baking powder and some oil.
When i have cake orders for children with egg allergies i use plain non-flavored gelatin. It works perfectly.
Of course!! Here is a website with tons of egg-free recipes :) [link removed]
sorry the link was removed-- just got to egglesscooking.com
Instead of egg use apple sause ! :) that's what I do