Hi, cool! Here are some answers:
1-the surface you'll come into contact with is plastic, whether the screen is matte or glossy.
2-I don't think you have to pair a remote with your computer, but it's a very quick and simple process anyway, so it's no big deal. Edit because mduell beat me to the post: You DO have to pair a remote with the various remote-capable iPod docks, and that's probably what I was thinking about.
3- I know nothing about Singapore, but a lot of authorized resellers make up for having fixed prices by offering free goodies, so you can probably find one there that will offer a sleeve or case. Look around.