Learn Russian: Двери закрываются в восемь часов.

The base verb закрывать means to close (like when a person closes a door). By adding the reflexive ending -ся, it takes on a passive meaning: the doors are being closed, or simply close. This is how you show the doors are the subject undergoing the action, without mentioning who is actually closing them.

Could I use the perfective form закроются instead?

You would use the perfective закроются if you were talking about a specific, one-time event in the future (the doors will close at eight today). Here, the imperfective закрываются is used because it describes a regular, repeating schedule: the doors close at eight every day.

Why do we say восемь часов and not восемь часа?

In Russian, numbers 5 and above require the noun that follows them to be in the genitive plural. So, the word час (hour) becomes часов. If it were two, three, or four o'clock, you would use the genitive singular часа.

What gender is the singular word дверь?

It is a feminine noun. Many nouns ending in a soft sign (-ь) are feminine, and they form their nominative plural by changing the -ь to an -и, which gives us двери.