Yeah, the coating is that shiny sort of spilled coke looking stuff that doesn't quite come all the way up to the connector end of the board.

Flux is an acidic sort of gel. It cleans the oxidation from the metal when you heat it up so the solder will stick better.

I wouldn't try to remove the coating. I recommend first heating each joint up one at a time. You will see some of the solder make a retreat as the coating boils away. After I had gotten about half way through my board, I found that the solder would stick better after I had sizzled the coating away first.

If you solder two pins together, don't freak out. You can easily fix that problem. The best thing is solder wick, but fresh fine copper wire works fine too. If you have some speaker wire laying around, you could hold that to the excess solder as you heat it all up. The solder will literally wick up onto the fresh copper.

Just take your time. The worst thing you can do is over heat the board or components. You shouldn't spend more than a second on each pin at a time. Do not keep going back to the same pin if you have a problem with it. Move on and come back to it once it has cooled. Too much heat will lift those pads that the pins connect to, or worse, damage one of the chips.

Oh, one more thing, get a fan to blow the fumes away. They give me a headache every time.