No, I'm afraid there's no way to make further folders inside the assets library.
One reason for this is that if you were to move things around then any links to them would no longer work. By simply not allowing people to move them we get around this problem! (crude but effective! :)
I admit that this can mean you end up with a rather large list of images all in the same folder, which isn't ideal.
Regarding the second point - while photo album images don't appear in the pop-up allowing you to easily select the image to insert, you can still add the image to a page:
Hope this helps!