Ok, I have used basically the same thing from Treatland. I do remember having to cut and change a connection (bullet style connectors) on the replacement in order to get it wired correctly. As I remember I cut one of the connectors off of the old bulb and wired to replacement. IIRC not all the wire colors matched either. This could explain the high/low beams working backwards on the switch in your situation. In the end mine has worked flawlessly. Have only replaced bulb inside new housing once in well over 2000 miles.
The other issues you are having are seperate from the headlight.(edited)