OK, there are obviously things going on that I don't understand, what with the non-chatting chat windows and such.
Alt-J doesn't do anything except sound a tone and give me a message saying that window can't be hidden; also, I hadn't hit alt-J when the quest helper disappeared. I hit the D key to turn right, and halfway through the turn, that window vanished.
Likewise the maintained spells, only I was turning left this time. By dint of much experimentation, I've finally managed to scroll them back into sight, but it didn't work until I had unlocked it, turned off click-through, made the background visible, and given it a frame. Then I could scroll the window (which has no scroll bars!) with the mouse wheel. I had never scrolled the window through any means of which I'm aware, though, so something odd happened to cause those spells to vanish off-screen.
Anyway, thanks for the hint, I didn't even know that was possible.
Oh, and while I'm here, I may as well ask: is there any way to turn off the highlighting of the hotbar buttons? The buttons remain highlighted when I remove the cursor, and the only way to get that off that I've found is to mouse over the little box at bottom right which activates window settings (and isn't visible now).