Well, you've got a couple of different issues here. Here's how I grouped things.
You need:
-a filing system
-a place for office supplies (tippex, highlighter, pens, ruler, hole punch, etc.)
-a place for personal stuff (nail clippers, hair grips, etc.)
-to put some things back where they belong (whiteboard pen, batteries, flute music, etc.)
-to either fix or toss some broken things.
First, the filing system. Do you have one at your other desk space? In which case, what you need here is a movable file box that you can carry back and forth. If you don't, can you use one drawer of the purple cabinet for your paperwork? The letter, postcards and list of textbooks can all then be filed away. Or maybe a two tier wire tray, with the top for "to go to other desk" and the bottom for "to be worked on." Or maybe what you need is a vertical file holder, that could hold various papers and the records. I guess my point is that the wire tray doesn't seem to be working and you should explore other options for holding paper on your desk.
There are small sets of plastic drawers that could hold all your office supplies: Tippex, highlighter, pens, scissors, USB cable for camera and MP3 player, ruler, holepunch, post-its, bookmark, string, rubber band. Get the right set and you can designate a drawer for the nail clippers, emery boards, kirby grips and hairpins. Or stash those in a pretty box.
Things that need to go back where they belong: whiteboard pen, batteries, staples, flute music, calculator, zip lock bags.
Things to be fixed or tossed: plastic cover for computer ports, broken MP3 player, screws for cable basket--either put the basket up or toss the screws or label them and store elsewhere for future use.
As for the coasters, get a set that stack neatly together when not in use and only have the number you need at the time out on your desk. Or maybe the extra ones could go in the storage drawers.
Can you get a better bookmooch box that is easier to use? I know, for me, that the harder it is to put something away, the greater the chances that it will never, ever, be put away. I deliberately look for easy to use (according to the way I will use it) storage. One time, on a decluttering TV show, they gave a guy who left his clothes all over the bedroom a new clothes hamper. A hamper with a lid, so he'd have to open it every time he used it (which I see as an extra step that isn't necessary). And then they put it in his closet, under a shelf. Now, in order to use that hamper, he'd have to open the closet, pull the hamper out from under the shelf (because it just barely fit under there and couldn't be used without pulling it out), and open the lid in order to toss anything in there. Any one of those (opening door, pulling out from shelf or opening lid) I could have lived with, but all three? I doubt that hamper got used much, at least not while it stayed in the closet.
If you put all the "foreign" stuff away and tossed the broken stuff, you'd be a pretty big step towards clearing the desk off.