How to say : That computer is being used by him.
I've recently learned that you could express the 'by x' part with 'x(In) tarafından'. So your sentence would be: 'Şu/o bilgisayar onun tarafından kullanılıyor'.
I'm only 89% certain though.
Why is bilgisayar in the normative case when it is object and a specific object?
It is not an object, but rather the subject :) This sentence is in the passive voice which never takes the accusative case (this is true across most languages I have studied as well).
Turkish grammar keeps getting harder. What gave me the idea that it would not?
Why can't we use the aorist form of kullanilmak here?
şirket işlerinde o bigisayar kullanılır (that computer is used for company works)
if you want to set up a sentence in aorist form, there shouldn't be -ing on verb in english translation
I know this falls beyond the scope of the course, but would 'kullanılmaktadır' be acceptable here as well?
"That computer is being used."
Translation: O bilgisayar kullanılıyor.
Şu bilgisayar kullanılıyor.
Also accepted as a correct Turkish answer by Duo.