If I froze the tiny amount of residual air(or cooled it to a liquid) in a vacuum tube and sent electrons inside, would the air still ionize? also how many atoms are in a milligram of air(I can find how many molecules via moles are in air online, but not atoms via moles)
To answer your first question: In calculations, we assume that vacuum has no air, so it won't ionize. But we are not good at creating a vacuum and there is always something left. So in that case, if the electrons happen to interact with those scattered air molecules then it will ionize. But of course, it depends on the type of "air". But then why are you freezing the air then?
To answer your second question: Look up Avogadro's number.