Longer shots.....it seems to correct itself.
Yep, the fletching drag starts kicking in and straightens things out.
Yep, I won't use a quiver attached to my longbows. Fully loaded with arrows, made it close to impossible to shoot well. It can cause you to torque your handle and get bad arrow flight.
I don't like bow mounted quivers either. When loaded up with arrows, it makes a bow feel really lop-sided and off balance to me. The only bow mounted quiver I've used is a Kwiky Kwiver that, once I get to my stand, I take off the bow and mount to the tree. I never shoot with it on the bow. I've never put one on a longbow. I opt for hip quivers instead.