Exactly, to make NA's appear as an own category you need to turn those into a factor. And this is no problem since you anway need to turn your numeric variables into groups (explicitly or implicitly). That being said, please keep in mind that bar plots are often not the best choice to show numeric, continuous values.
The {naniar} package is an interesting package to work with NA's so maybe you have a look.
With regard to your text labels (I guess this is what you mean by "showing the coutns"?) a working example is needed as @zac-garland already mentioned. So please provide the data as well so we can try it on our own.
The problem is exactly that I have a big data sheet from excel. When I imported it in R Studio, the columns which had had categorical responses coded as numbers (1,2,3,4,5) - i.e. most of the columns - got imported as "double". Wanted to get the counts without changing the type of variables as it would be quite laborious. I needed the counts of 1s, 2s and so on.
Actually, a solution to another problem (with names) somewhat hindered me in finding a better solution here, I will post it below.