How to move layers around?

If it's a single image (1 big tile) you can use the nudge tool. If it's a tiled document you can only move in tile increments.
(You can also use the marquee selection tool but I wouldn't recommend it because it's not fully implemented yet.)

Thanks for the reply, I meant "re-ordering" layers though. The question wasn't very clear. I figured it out though, I used CTRL+Left Click to drag them around.

actually you can just drag and drop them. The same with tiles :) no ctrl needed.

Yeah, you should be able to just drag and drop them.

Whoops, you're right. I guess a "dragging ghost" would help here (unless that already exists and it's just not displayed under Wine).

That's a good idea, or at least a different mouse cursor.

BTW, how well does it run under Wine? Are there any issues?

So far no issues encountered. It runs as well as a native GNU/Linux program, which is surprising! 

Yeah, that is quite surprising. Thanks for the info!