Learn Russian: Каждый пользователь может открыть любой файл.

Каждый means "every" or "each," pointing to all individuals in a group one by one (every single user). Любой means "any," emphasizing free choice (whichever file they want to pick). If the sentence said любой пользователь, it would mean "any user (whoever you pick)." If it said каждый файл, it would mean they can open "every single file."

Любой файл is the direct object of the verb, so shouldn't любой be in the accusative case?

It actually is in the accusative case! Because файл is a masculine inanimate noun, its accusative form is identical to its nominative (dictionary) form. The pronoun любой copies this behavior, so its masculine inanimate accusative form remains любой.

How do we know the gender of a soft-sign noun like пользователь just by looking at this sentence?

You can tell it is masculine because the pronoun attached to it is каждый, which has the masculine -ый ending. Also, nouns ending in the suffix -тель (which usually denotes a person doing an action, like a "user" or "teacher") are always masculine.

Why does the sentence use the perfective verb открыть instead of the imperfective открывать?

The perfective открыть is used because it focuses on the result: the successful completion of opening a file. If we used открывать, it would imply the physical process of opening it, or a repeated habitual action. Here, the focus is purely on the ability to successfully get the file open.