The male connectors do have the pins in them, but be very careful soldering to them as the plastic has a tendency to melt. I recommend removing the pins, trimming them down, soldering, heat shrinking, and reinserting them. They just pull straight out.
It looks to me that several of your halo bulbs are burned out. They are quite a bit dimmer than the backlight, but they should be pretty noticeable either way.
Any electronic store or auto parts store will have it. Otherwise there is always Amazon or even Mouser.com