I’ve never had a door pop but I once departed with some seatbelt webbing closed in the door. I had moved the pax seat forward for some reason and the part of the door with the belt tail hanging out was on scurry from view. At some point in the climb, I heard a slapping noise. Took a few seconds to realized what I had done. At about 3k I slowed to 100mias. I then opened the pilot side window (don’t think it mattered one bit given the size of the cabin vents but remember reading about it so I did it). I then unlatched the door, retrieved the seat belt tail and closed the door. It was not difficult at all. I have very good mating between door jam and door (absolutely no leaks) so maybe that helped.
As to ASI increase with door opening, you raise an interesting question that leads me to believe that my alternate static source is open. If I open the pilot side window in flight, my indicated altitude jumps about 80ft and my IAS jumps a few knots.