There is no relationship between H1 and the other bulbs. The connector(base) is different.
9005 and 9006 differ very slightly. Their bases are different by way of a little notch on the base of the bulb, so if that notch is sanded, it can fit in a 9006 socket.
That adaptor is proper fitment into the headlamp reflector hole. The projector itself only uses an H1 HID bulb.