Learn Hardcore Russian: Она должна приготовить ужин сегодня вечером.

Должна is a modal adjective meaning “must” or “have to.” It expresses necessity and is used with an infinitive (приготовить) to say that doing something is required.

Why is должна in the feminine form?

Because the subject она (“she”) is feminine. Russian modal adjectives должен/должна/должно/должны agree in gender and number with their subject. For “he must” you would say он должен, for “they must” они должны, etc.

Why is the perfective infinitive приготовить used here instead of the imperfective готовить?

Russian has two aspects:
• Perfective (приготовить) indicates a completed action (“to cook and finish”).
• Imperfective (готовить) indicates an ongoing or habitual action (“to be cooking” or “to cook regularly”).
Since the sentence refers to preparing dinner as a single, completed event tonight, the perfective приготовить is appropriate.

How would I make this sentence negative?

Simply insert не before the modal adjective:
Она не должна приготовить ужин сегодня вечером.
This means “She doesn’t have to cook dinner tonight.”

Can I move сегодня вечером to the beginning of the sentence?

Yes. Russian word order is relatively flexible for adverbials:
Сегодня вечером она должна приготовить ужин.
The meaning does not change, though starting with сегодня вечером can add emphasis to the time.

How do I turn this into a yes/no question?

Option 1: Raise intonation and add a question mark:
Она должна приготовить ужин сегодня вечером?
Option 2: Use the particle ли for a neutral question:
Должна ли она приготовить ужин сегодня вечером?

What case is ужин in, and why doesn’t it change?

Here ужин (“dinner”) is the direct object of the verb. It’s masculine and inanimate, so its accusative form is identical to its nominative form. Hence ужин stays the same.

What’s the difference between using должна + infinitive and надо + infinitive (or + dative)?

Both express necessity, but:
• Она должна приготовить ужин uses the modal adjective должна and nominative subject.
• Ей надо приготовить ужин uses the impersonal construction надо + dative (ей) + infinitive.
They’re largely interchangeable, though надо constructions are often more colloquial.