Qual è la differenza tra 뭐 하고있어? e 뭐 하는 거야? ?Sentiti libero di rispondere con un esempio.

The actual meaning of '뭐 하고 있어?' and '뭐 하는 거야?' is same as 'What are you doing now?', but there is nuance.

When you use '뭐 하고 있어?', It's kind of checking (asking) what the other party is doing now.
For example, A: 뭐 하고 있어? (What are you doing now?)
B: I'm just chilling on my bed. Why?
A: Let's meet up!

But when you say '뭐 하는 거야?', It could be interpreted two ways.
1) To ask someone what he/she is doing now in front of you, with curiosity.
A: (drawing something whatever you don't understand what it is)
B: 뭐 하는 거야? (What are you doing now?)

2) To blame his/her improper action (in embarrassed, or upset situation).
A: (Pickpocketing in front of you)
B: ??? 뭐 하는 거야? (What are you doing?)
-> In this case, 뭐 하는 거야? can be replaced by 무슨 짓이야?