Correct, but in a longwinded way
Incorrect, sorry! Earth rotation not involved, atmospheric circulation is primarily the result of a complex-ish interaction between atmospheric and oceanic circulation, caused by heating and cooling and, in the case of oceans, variations in water density (salinity) which is also partly the result of temperature variations.
Atmospheric circulation is primarily the result of oceanic circulation - take the example of the El Nino variation in Pacific Ocean circulation and the effect that this can have on global weather patterns.