"Avoided the attack" is when the move targets more than one Pokemon. "Missed" is when it targets just one Pokemon.
This is correct. It has nothing to do with accuracy or evasiveness.
If the move that was used targets more than one Pokemon in 2v2 battles, it will say "(Target) avoided the attack!". If it only targets one Pokemon in 2v2, it will say "(User)'s attack missed!". This happens even in 1v1 battles now, for some reason.
Remix? Contrary to popular belief, I do, in fact, exist.