Let us consider a situation -
Suppose you have a best friend who is in desperate need for money. But instead of asking you for help he goes ahead tries to steal the money from someone's house and gets arrested in the process. Now when you go to visit him in a prison what question would you ask him from the following two ?
- Why did you steal the money ?
- Why would you steal the money ?
When you ask 'Why did you steal the money ?' you demand an answer. Plain, simple, logical answer.
But when you ask 'Why would you steal the money ?' - here you do not demand or expect an answer. But you are simply expressing your disbelief, suprise or shock on this stealing thing done by you best friend. You might indirectly be suggesting him that 'you could have asked me for money. I might have been able to help you out.'
Consider another situation
Suppose one of your friend has broken up with his girlfriend recently. But still he goes ahead and buys a gift for x-girlfriend on her birthday. This thing does not make sense to you. Now which question would you ask him
- Why did you give her a gift ?
- Why would you give her a gift ?
You won't for sure ask him the first question because you do not want to know the answer. You'd ask him the second question as you are simply expressing your disbelief, suprise or shock, because him giving gift to his ex-girlfriend after having broken up with her does not make sense to you.
In the above examples 'would' is used when something does not make sense to you as I guess in your example something doesn't make sense to Josh Brolin.
There is also a very important difference that we need to take into consideration. In both of the above examples 'things / events have really happened in the past.' But what if these events are in future which might happen but have not happened - then also the second sentence in both the examples will remain the same with difference in meaning. In that case 'would' will be used as past tense of will.
Lets modify the first situation for a better understanding
Suppose your friend lets you know beforehand that he is going to steal the money. (Assuming you also are not in a position to help him) Now you say -
Why would you steal the money ? (You might ask others for help or you might look out for alternate ways)
And in the second example you say -
Why would you give her a gift ? (You don't need to give her a gift now that you have broken up)
Note - The 'would' question used for the events happened in the past and the events that might happen in future remains the same. However feelings of disbelief, surprise, shock or wonder remain same in both the tenses, because in such kind of situations 'would' is used when something doesn't make sense to you.
The 'would' question can be used referring to the past or the future. (Please refer the above answer)
However here we are talking not about the unrealised future but the actual past. So I will only post the answer with reference to the event that has actually happened.
Let's again suppose you are a policeman investigating a burglary in the rich neighboorhood and one of the suspects is the neighbour who happens to be rich and you found his fingerprints inside the house where burglary took place. Now you may use 'would' or 'would have' as per the context
1. To express disbelief, surprise or shock
Why would he steal the money when he is already so rich ? (This means - the thing that 'the rich neighbour stealing the money' doesn't make sense to you. But still you officially know that the neighbor is the thief. Here you are only expressing disbelief and may not need to find out the answer. Because you might have assumed that he is extremely greedy.)
2. To really find out the answer to the question -
Here you might be needing to find out his real motive behind the burglary. It may not be the money but something else. Now you say
Why would he have stolen the money ? (Maybe to throw the police off the scent and hide another crime.) Unlike the first sentence, you need to find out the answer here.
So your doubt 'So why would have done is used here instead of would do?' -
Both questions are possible except that you need to establish the context.