Learn Russian: Новый кинотеатр открыли вчера.

Russian often uses the "they" form of a verb without the actual pronoun они (they) to show that an action was done by unspecified people. This is a common way to express English passive phrases like "was opened" or events where the actor isn't important. Literally, this sentence means "(They) opened the new cinema yesterday."

Is Новый кинотеатр the subject of this sentence?

No, it is the direct object receiving the action, so it is in the accusative case. Because кинотеатр is a masculine inanimate noun, its accusative form looks exactly the same as its nominative (subject) form.

Could I use the reflexive verb открылся instead of открыли here?

Yes, you could say Новый кинотеатр открылся вчера. Both are perfectly natural. Using открыли focuses slightly more on the fact that an organization or people launched it, while открылся focuses simply on the business starting its operations.

Why is вчера placed at the very end of the sentence?

In Russian, the newest or most emphasized piece of information typically goes at the end of a sentence. By placing вчера last, the speaker is emphasizing when the cinema was opened. If they wanted to emphasize what opened yesterday, they would likely say Вчера открыли новый кинотеатр.