A [very basic?] question about light scattering and colors Since the night two days ago, the moon here in Israel appears to be orange as it rises, and then gradually becomes white as it continues travelling across the sky.   

This phenomenon comes in a great timing as I am starting to become interested in astronomy (I have no special knowledge in astronomy, just to make it clear).
So I googled up and came across this explanation.
I'll try to summarize: it says that it happens because of Earth's atmosphere, that tends to scatter short wave-lengths (such as blue and green) and let long wave-lengths (such as red and orange) pass through. When the moon rises, it's in the position where the light coming from it to our eyes goes through the thickest layer of atmosphere (as opposed to when it's high up in the night skies) and that gives the orange effect. 
I totally get this explanation, but it raises a couple of questions for me, whose answers I couldn't find. Maybe you could help me out. 


Why doesn't the orange moon phenomenon occur all the time?
It does not happen quite often. What's so special about the past three nights? I mean, the rising moon's light always has to go through a thick atmosphere layer, doesn't it?
Maybe that's not entirely astronomic, but, to complete the big picture - why does our atmosphere scatter short wave-lengths?
This explanation suggests that all light coming to us from the sun is (at least) slightly reddish. Is this measurable (if true)? Because to the naked eye, sunlight refrected through a prism shows no tendency towards red. 


Thank you for your time reading the question, I hope you could rescue me from my ignorance...
There may be a particular effect. Smoke from wildfires or cities, fine dust in the atmosphere etc. can have the effect of making the moon appear redder. However it is most likely an example of observation bias.  You noted that the moon appeared orange, and on subsequent nights you were looking for this effect. In fact it happens each moon rise. You just didn't notice it before (or if you did, it didn't make enough of an impression on you.)
There are two forms of scattering that are applicable. Rayleigh scattering, and Mie scattering. There is also absorption of some colours. Rayleigh scattering occurs as the electromagnetic wave that is light causes the molecules of the air to act like little electic dipoles. The light then bounces of these electrically active molecules. Shorter wavelengths are affected more than longer ones.
The light emitted by the sun is very slightly yellow. It is slightly reddened by scattering through the atmosphere. However it still contains a mixture of all visible colours, and so a prism will still show a complete rainbow. The reddening is not apparent to the eye, but can be measured by instruments.