how can I find out about the filename and filetype (png or jpg) of an imported background image of a room?
(Correct me if I am wrong) you cannot. These information are lost after import.
The background images aren't stored as-is like the original file. Instead they're recompressed (not using lossy compression like JPEG so it's safe) with AGS's own scheme to be embedded in a room file. So it's not a wise thing to do in importing JPEG images as background as this won't help in saving disk space.
meh, too bad. But good to know, so the final BG will be png then ;)
Yeah. It's recommended to use non-lossily compressed images for import. PNG is one perfect choice.