Here are some pictures.
What makes it difficult to swap the bulbs is that the wires runs through a rubber grommet that's located on the headlight cover. The connector is on the outside of the cover. I can't pull the wire through the grommet as the connector is too big. I can't swap the entire grommet wire/bulb assembly as the driver side is different from the passenger side. What I ended up doing (what I really didn't want to do) was to cut the wire between the bulb and the rubber grommet and adding a connector there. I guess I would have to do that eventually as I wouldn't be able to feed the new bulb/wire/connector through the grommet. After doing that I was able to swap the bulb and indeed the problem is the bulb. What is the HID bulb size/type? Alpine's HID bulbs are $25/ea. Ebay has a pair for $15.
2nd question. I still don't know why my inner headlights won't light up when I flash my high beams =(