Being able to claim multiple blueprints from playing the same mission over and over seems to be a rare bug. I've heard someone else talk about it before but never had it myself. If it works, great, get you some BP's, but it would be a bug of some sort.
Rare BP's appear on the missions the same as common BP's, and appear more frequently at higher levels.
Level will dictate your Aequilibrium tier. People in the same tier will have the same rewards scattered around the missions. People in the same GROUP (the player names you see when clicking on the aequilibrium) within the tier will have the same rewards on the same missions. You have no way of controlling what group you get in as the game will move people around randomly and we have not gotten an explanation of how the mechanic fully works, so we can only guess geography and MMR might place you into a different group.