Learn Russian: Вы должны предупреждать менеджера за два дня до встречи. - You must warn the manager two days before the meeting.

This follows the pattern you are learning: за + Accusative for the amount of time + до + Genitive for the event. The amount of time is два дня (two days), and the event is встречи (the Genitive singular form of встреча, meaning 'meeting').

In the phrase за два дня, is the word дня in the Accusative case?

The whole phrase два дня is in the Accusative case to satisfy the preposition за. However, because of Russian number rules, the number два forces the noun directly after it to be in the Genitive singular. So, дня itself is Genitive singular (from день).

Why is the imperfective verb предупреждать used here instead of the perfective предупредить?

Using the imperfective shows that this is a general, recurring rule: you must always or routinely warn the manager. If this sentence were an instruction about one specific, upcoming meeting, it would use the perfective предупредить.

Why does the word for manager look like it is in the Genitive case (менеджера)?