Why would it not be "Tam olarak yapiyor mu?"
The question is not a "yes-no" question. If there is a question word like "what" you have to use it.
I think that would be "Is he doing, exactly?"
Why do we need to add "olarak" when we didn't use it for the sentence just before and the meaning was quite the same?
"olarak" is optional. "Tam ne yapıyor?" is also accepted. :-)
What's wrong with O tamamen ne yapıyor?
"What exactly is he doing?"
Translation: Tam olarak ne yapıyor?
Tam olarak o ne yapıyor? - Accepted answer.
Why kesinlikle is wrong?
tam olarak = exactly /specifically (What exactly is an owl? Baykuş tam olarak nedir?)
kesinlikle = definitely /certainly (An owl is definitely a bird.
Baykuş kesinlikle bir kuştur.)