BKS,
In response to (2), it is largely a question of the limitations of only having 3 letters. Many of the best are already taken, so I presume BirmingHaM Al had first dibbs on BHM, although BIR went to Biratnagar, Nepal, well down the pecking order.
DXB is unusual in that the extra letter is in the middle.
So my guess for MME is that the double M is either superflous, or it is for Middlesbrough + Middleton, both of which could have used ME.
I also presume PMI = Palma, Majorca, Island, and MNI = Montserrat Island, similar for GCI & ACI, the C for Channel.