You don't remove it. You have to paint over it.
Warm water, soap and a scrub brush should do it.
Paint or Stucco
NO, it will not penetrate.
It depends on your location and the quality of paint. A gallon of exterior stucco paint will cost anywhere from $15 to $65. $30 in 2012 should buy a very good quality paint that will give you several years of service.
YES, but first remove any loose or flaking paint then make sure the surface is clean and free of dirt, then you must apply a bonding agent (glue) a.k.a. concrete bonding adhesive, this can be done just like painting with a paint roller. MAKE SURE YOU COVER ENTIRE AREA WITH ADHESIVE BECAUSE IF YOU MISS A SPOT YOUR FRESH COAT OF STUCCO WILL LIKELY CHIP OR FLAKE OFF!
Built of stone and covered with stucco and polychrome paint
use something soft like a sponge to help
If they are about the same size, yes, because wood is much more absorbent than the mortar of stucco by far.
Diluted bleach can clean stone brick stucco. Often gentle water pressure can remove hard water stains on stucco as well.
For smaller repair jobs, simply fill damaged stucco with paintable caulking, using your fingers to blend in with pattern of the stucco. For larger jobs, first soak area with hose, then use wire brush and chisel to clean out loose debris. Purchase a stucco repair product such as DAP Premixed Stucco Patch, follow the manufacturer's instructions, allow to dry, then paint, if necessary, to match the surrounding stucco.
To repair stucco, first you must have a mixture of wet stucco to be applied. Sometime you can find it premixed and other times you must mix it yourself. You next remove all of the loose stucce until all of the stucco on the wall is firmly stuck to its lath. Then, you replace the paper and the metal mesh. Next you would slather on the wet stucco and smooth out.
Paint thinner will remove it.