Learn Polish: Nowy lider musi motywować wszystkich. - The new leader must motivate everyone.

The verb motywować takes the Accusative case. Why is wszystkich used here if this lesson is about the Genitive, Dative, Instrumental, and Locative cases?

You are right that motywować requires the Accusative case for its direct object. However, in Polish, for masculine personal (virile) nouns and pronouns, the Accusative form is identical to the Genitive form. So, the Accusative of wszyscy is wszystkich, which is the exact same word you are learning for the Genitive (and Locative) cases!

Would I still use wszystkich if the group of people being motivated is entirely female?

No. If you are specifically talking about an all-female or non-masculine group, the base pronoun is wszystkie, and its Accusative form is also wszystkie. You only use wszystkich when the group includes at least one male, which triggers the masculine personal (virile) forms.

Could wszystkich also translate to 'all' instead of 'everyone'?

Yes! When used on its own like in this sentence, wszystkich means 'everyone' in the required case. But it can also act as an adjective meaning 'all' when placed before a noun. For example, motywować wszystkich pracowników means to motivate all employees.

Why is the verb motywować in its imperfective form here?