1- One of the solutions is to wash the face or the arm directly under the water tap, from top to bottom, then you can wipe the place quickly, put a ready opened plaster, then continue your wudhu.
If this is not possible, you can wait till it stops, then perform wudhu.
If you are afraid that time will pass before it stops, then you can perform wudhu jabeera, by washing the surroundings only, leaving the wounded area.
2- You do not need to wash the plaster. It is enough to wash the surroundings , as long the plaster is not much bigger than the effected area.
3- If you did not follow what I said, then yes.