...So the 918 was manufactured after the 920 and 922? Did the 918 have the elinvar hairspring? (1941).

The 918 was after the 920. Production began a few years after the 922 but then was roughly concurrent. I do not recall ever seeing one with an elinvar hairspring.

Here is a 918 since the image at the top has expired.

Stem view (The case was open in the back, so a gap appears)

Front view