Tsagaan sar usually lasts 15 days. It just in cities people usually celebrate for few days. In countryside that usually lasts some 10+ days. About flicking vodka thing we are essentially saying that peace be with Eternal Blue Sky, peace be with Nation(or People), peace be with Mother Earth.
The reason mongols shake hands when stepped on someones foot is not because the floor is dirty. The real reason if you hit or step on someones foot is it is a bad omen that "you might quarrel over something, or some reason with that person". And shaking hands will protect you from quarreling with that person. It is just a custom.
