Questions about scalogram and wavelets

[TecHNooB]

1.) What is meant by vanishing moments? Is this a moment in time or moment in regards to weights?
2.) Which wavelet should you use to construct a scalogram?
3.) Why do wavelets like Haar chop the frequency the way they do? Why not make even chops. My motivation is toward the construction of a scalogram using wavelets so if it's a compression thing then I completely understand.
4.) Why are wavelet values called coefficients when they're actually waves (ie. a vector of values)?

Thanks