Why are there..? is the normal direct question form. Why are there so many cars parked outside that house? (What is the reason?) 'Why there are' is a statement. 'I am going to tell you why there are so many cars parked outside that house.' (I am going to tell you the reason) 'Why there are' can also be used in an indirect question. 'Could you tell me why there are so many cars parked outside that house?' (Could you tell me the reason)

"why are there...?" is a direct question. "Why there are..." is statement posed as a question. For example, "why are there so many people in the restaurant?" You don't know the reason and therefore you asked the question. "Why there are so many people in the restaurant" is a statement asked as a question. You already know the answer but wanted to see if the person you spoke to knows the reason as well. It's more of a rhetorical device.

Both are correct. It depends what you want to say.

both are right. Its depends what you want to use. :) :)