Looks like my Windows XP has suddently started integrating my Mozilla Thunderbird into the Explorer…

haha, yea. My FireFox did that once. Im not quite sure why, just happened all of a sudden one time.
Funny, I have similar things constantly. Apps being put behind the explorer (as in your example), windows disappearing, etc. Sometimes a window disappears totally, but without the app closing. When I minimize all other opened windows to the taskbar the disappeared window suddenly appears again.. very strange. Like xp can't handle all those opened windows and is confused. Maybe rename it "search-the-windows xp"?? :)