Can someone explain the calamities/shards/source thing?

[LostLogia4]

So the 7th calamity was non-elemental? Meteor/bahamut?

Technically Bahamut is aspected towards flare, which is related to fire but is outside the element cycle. In practical terms it is treated as a non-elemental aether, as Bahamut always had been represented in most FF games.