Let's use できる as an example.
できる (I) can do (it)/possible (action/event). できるか? Can do?/Possible? できますか? Can do?/Possible? (polite)
Believe it or not, できますか? still sounds too direct to me.
Now here's my question, is this dekimasuka?:
(もし)できますでしょうか? Possibly can do?/Perhaps possible? and (もし)できませんでしょうか? Can't (you) possibly do?/Isn't it perhaps possible?
If the above statements are grammatically sound, how about natively? When a native person hears it, what is their average response to such a statement/question?
Another related question: according to some teachers of Japanese, the か at the end of a question could be considered harsh, too direct or unnecessary. For example, what is the difference (if any) between [たべる?] (with question mark) and [たべるか?] (with question mark and か)?
Optional question: Where does だろうか? and でありますか?/でありませんか? fit into all of this?