Learn Russian: Вчера я не мог получить документ от менеджера. - Yesterday I couldn't get the document from the manager.

We use от because the document is coming from a person (the manager). You use от to mean 'from a person' or 'away from a person/object'. You would use из if you were taking the document 'out of' an enclosed space, like a folder or a room.

Why does менеджер change to менеджера?

The preposition от always requires the Genitive case. Since менеджер is a masculine noun ending in a consonant, you form its Genitive by adding -а to the end.

Документ is the direct object here. Why doesn't its ending change?

It is actually in the Accusative case. However, because документ is a masculine inanimate noun (a non-living thing), its Accusative form looks exactly the same as its standard dictionary form.

Why use the perfective verb получить instead of the imperfective получать?

You use the perfective получить because the focus is on the result of a single, completed action—successfully getting that specific document—rather than the general process of receiving things.

How do we know if a man or a woman is saying this sentence?