I would suggest making the batter, then scoop the batter into sandwich bags, add the food coloring, mix it up and then you can cut off the corner and pour into cupcake liners. That would be the easiest for cleanup and save yourself from washing a bunch of bowls that you mixed the food coloring in.
Layer the different color batters and bake. While you are baking you can make the icing.
For the icing: I use real butter for the frosting...gotta use the real stuff! Cream butter until light and fluffy. Add sugar 1 cup at a time mixing well. Add milk and vanilla. Then whip until it's light and fluffy...really, keep whipping! Spoon frosting into a quart sized baggie, snip one corner of the bag and pipe the frosting in swirls on top of the cupcake.