One way to see that the version without the preposition is special is to see that it can only be used in the imperative.
That's a very good point, David.
Yasukotta, let me give you my view on your new sentences:
(4) Take a look what you've done!
That's wrong. You always need "at" after the noun "look": Take a look at what you've done!
(5) a. Look how much money he makes!
b. Look the amount of money he makes!
(5)a sounds strange but seems to be grammatically correct, while (5)b is not. You need a nominal clause after "look" to be able to drop the preposition "at."
(6) Listen what they are saying!
You need "to" after "listen" even if a wh-clause follows: Listen to what they are saying!