Axis & Allies Developer and Playtester; War of the Ring Editor and Playtester
Now it has been quite a while and do not remember 100% but I think it was they had the actual box art that was used on the game but released a different version of the box art prior to the official release. Since the image was available, it was taken and reused on the web even though in the end it was not correct.
This is correct. The "1942" cover was a prototype version that was used in pre-release publicity but never produced. The "1941" cover is the actual production one.
It is further complicated since they have released multiple Deluxe Anniversary Editions of the game so finding the correct one by searches can be a challenge.
This is not so correct. There is only one Anniversary Edition. However, there have been a few different editions since then, including Axis & Allies 1941 (an "entry level" version), Axis & Allies: 1942 (the current "flagship" version), and Axis & Allies Europe 1940 and Axis & Allies Pacific 1940 ("deluxe" versions that can be combined into a monster global game).