The artist knows flint lock rifle and what they look like, so, that is what they draw. The artist does not know airguns, so, they are not drawn. It's about impossible for an artist to draw something that they are not aware of.
Yes and no - the airrifle is depicted in contemporary prints - as well as the carbine system Crespi.
Seemingly air rifles were produced well into the mid 19th century, as for example by Oesterlein in Vienna, and not only guns but pistols as well.