Learn Russian: Почему ты выбираешь этот скучный фильм?

No. Почему is the question word specifically used to ask "why?". Потому что means "because" and is used in the answer to give the reason. You will always start a question like this with почему.

Since "this boring film" is the object being chosen, shouldn't этот скучный фильм change its endings for the accusative case?

It actually is in the accusative case here! For masculine nouns that are inanimate (objects, not living things), the accusative case looks exactly the same as the nominative (dictionary) form. So, этот скучный фильм doesn't need to change its endings.

How do we know the sentence means "Why are you choosing" rather than "Why do you choose"?

Russian doesn't have a separate "-ing" (continuous) tense like English does. The single present tense verb выбираешь covers both "you choose" and "you are choosing". You just rely on the context to know which translation sounds best in English.

Why is скучный pronounced with an "sh" sound instead of a "ch" sound?

The letter combination чн is traditionally pronounced as "шн" (shn) in several very common Russian words. Скучный (boring) and конечно (of course) are two of the most frequent examples where you'll hear this exception.