I'm not a teacher.
Q1: CMD = From the context of the paragraph, it seems that "CMD" is refering to David Cameron, though I cannot explain why!
Q2: 'get down with the folks in the hood. = This means to appeal to the lower social classes. "The hood" is slang for a deprived area - a ghetto.
Q3: 'These guys just chalk your diary up.' = I think it means to keep busy, to keep a diary full of appointments - but I'm not sure.
Q4: What does the columnist mean for " Doesn't sound very Old Etonian to me"? I knew David Cameron is an old Etonian. I think it means that the kind of language Cameron used was not typical of an Etonian (or more generally, a well spoken English person). It is meant to draw attention to the fact that Cameron spoke in a more American manner to help encourage and create a better political relationship with Obama.