8.  Can I paint stucco?  If so, with what? 
    If not, how do I clean it or change the

Stucco should only be painted as a last resort and very carefully.  For 50 years the common expression has been that you should not paint stucco.  Why?...because paint would not stick to stucco.  The high alkalinity, the powdery finish, the lime wash, the loose rocks made it hard to paint well, or for paint to last. So it was a frustrating process….after going perhaps 30-40-50 years on a stucco finish and doing almost nothing to it…they would paint it…and then in just 5 years or less they would have to re-paint it…again and again….but often times the paint from the first coat would be flaking and peeling and make a re-paint very difficult.
Now, we have a different problem.  The paint is too good.  Today's acrylic paints, the oil based paints, the liquid vinyl paints and the 'elastomerics' can stick to almost anything.  They fill in all the pores and bond completely to the cement stucco finish.  This forms a waterproof or almost waterproof face seal.  Now the stucco can no longer breathe out its moisture from the last rain storm….remember the plastic sealed sponge.  They say they are breathable…and they are but not enough…as one manufacturer told me…remember…a pillow is very porous and breathable…but you can smother someone with a pillow.
So if you paint stucco then you begin to reduce the breathability of the stucco finish and water is more likely to be trapped behind the finish.  The denser the paint…the more plasticity it has….the more it will trap moisture and slow down evaporation.  The water-based acrylic latex paint has higher breathability than the oil based paints or the elastomeric/vinyl paints.  However, even today's acrylic latex paints are of such good quality that they also reduce that vital breathability.  Then, if it is later painted to change the colour or spruce it up…..now you have probably 4 coats….2 coats each time…that combine to further reduce the breathability. 
How do you know if a finish is painted?  Chip a little piece off with a knife or your thumb nail….that will allow you to see if the colour is changed or if the surface is smoother more sealed that the back side of the piece chipped off.  If the finish of the stucco shows an in-fill on the texture…this usually means it is painted.  If the finish does not absorb water then that means that it is probably painted or sealed…which can be just as dangerous.  Spray a bit of water onto the surface and observe if the water is absorbed or if the stucco darkens colour…indicating water in the finish.
How do you clean the stucco if it is dirty and dingy?  Usually stucco gets dusty and dingy looking….it may have moldy sections or black or grey mildew or green algae accumulating under windows or on the north walls….or where water splashes against the stucco….or where shrubs are close to the stucco wall. 
Most of these conditions are organic dirt.  That means that the surface for whatever reason is remaining moist long enough for these organisms to grow.  If it is that kind of staining then it can be cleaned by killing the organism and washing away the residue.  To determine if it is organic dirt…a small amount of household bleach can be brushed onto a section mixed 50/50 with water and left to stand for a few minutes then rinsed with a hose or glass of warm water.  If it organic…you should see a marked improvement on the section bleached….be sure to rinse the area well so the bleach does not damage the stucco.  Probably 90% of dirty stucco is caused by organic staining and marking.
The actual cleaning treatment for the stucco is to use a product called “30 seconds” or Behr mildew cleaner…or a solution of household bleach and tsp and tide laundry detergent…this formulation is a bit trickier.  The 30 seconds….you just spray it on and then 30 seconds later it starts to clean….wait about 5-10 minutes and wash it off with a pistol on your garden hose…hot water is best if you can hook up to the laundry tap.  Just follow the directions on the jug...be careful, it's caustic!