В аэропорту я должен сдать багаж.

Because аэропорт has a special location form after в when it means in/at the airport: в аэропорту.

This is an old pattern that survives with some masculine nouns, especially places:

• в лесу = in the forest
• на мосту = on the bridge
• в порту = in the port
• в аэропорту = at the airport

So this is not the ordinary prepositional ending -е, but a special locative-type ending -у.

It is traditionally called the prepositional case, though more specifically many grammars treat forms like в аэропорту as a special locative use.

Here, в means in/at, so it takes a location form:

• в аэропорту = at the airport

Compare:

• в аэропорт = to the airport
• в аэропорту = at the airport

So the case/form helps show the difference between movement toward a place and location in a place.

Багаж is the direct object, so it is in the accusative case.

But for inanimate masculine singular nouns, the accusative usually looks exactly like the nominative:

• nominative: багаж
• accusative: багаж

So the form does not change, even though the case does.

Compare:

• Я вижу стол. = I see the table.
• Я должен сдать багаж. = I must check in the luggage.

Both стол and багаж are masculine inanimate nouns, so the accusative looks the same as the basic dictionary form.

Должен means must, have to, or am supposed to.

In this sentence, it expresses obligation:

• я должен сдать багаж = I must / have to check in my luggage

Grammatically, должен is a short-form adjective used like a modal word. It changes for gender and number:

• я должен = I must (male speaker)
• я должна = I must (female speaker)
• оно должно = it must
• мы должны = we must

So if a woman is speaking, she would say:

• В аэропорту я должна сдать багаж.

Because сдать is perfective, and here the speaker is talking about one complete action: handing in / checking in the luggage.

Russian often uses the perfective infinitive after words of obligation when the focus is on completing the action:

• Я должен сдать багаж. = I must check in the luggage.

Compare:

• сдавать = imperfective, process / repeated action / general activity
• сдать = perfective, complete the action once

So:

• Я должен сдавать багаж каждый раз. = I have to check in luggage every time.
• Я должен сдать багаж сейчас. = I have to check in the luggage now.

No. Сдать is a very common verb with several meanings depending on context. Its core idea is often hand over, submit, or turn in.

Examples:

• сдать экзамен = pass an exam
• сдать документы = submit documents
• сдать квартиру = rent out an apartment
• сдать багаж = check in luggage / hand in luggage

So in an airport context, сдать багаж is the normal way to say check in luggage.

Russian can sometimes omit subject pronouns, but here я is very natural and often helpful.

One reason is that должен shows gender and number, but not clearly person in the same way a fully conjugated verb does. So я makes the subject explicit:

• Я должен сдать багаж.

Without я, the sentence can still be possible in context:

• В аэропорту должен сдать багаж.

But on its own, that sounds less complete and less natural for a learner’s basic example. Using я is the safest and clearest choice.

Russian word order is flexible. Putting В аэропорту first sets the scene or context:

• At the airport, I have to check in my luggage.

This is very natural in Russian. The sentence could also be rearranged:

• Я должен сдать багаж в аэропорту.
• Багаж я должен сдать в аэропорту.

These all mean roughly the same thing, but the emphasis changes:

• В аэропорту... = setting first
• Я должен... = focus on the speaker’s obligation
• Багаж... = focus on the luggage

No, not in this sentence.

Although должен comes historically from the idea of owing, in modern Russian я должен + infinitive normally means I must / I have to do something.

So:

• я должен сдать багаж = I must check in the luggage

If you want to say I owe someone something, Russian usually uses forms like:

• Я должен ему деньги. = I owe him money.

So the structure matters:

• должен + infinitive = must do
• должен + noun = owe

Grammatically, багаж is singular, but like English luggage, it often refers to baggage as a mass noun, not just one single item.

So:

• багаж = luggage / baggage

Even if you have several bags, Russian can still use багаж:

• Я должен сдать багаж.

If you want to be more specific about individual items, you might say:

• чемоданы = suitcases
• сумки = bags

Yes. That is also very common.

Compare:

• Я должен сдать багаж. = I must / I am obliged to check in the luggage.
• Мне нужно сдать багаж. = I need to check in the luggage.

The difference is subtle:

• должен often sounds more like obligation or duty
• нужно often sounds more neutral, like it is necessary

Both are correct, but должен can feel a bit stronger or more personal.

Because Russian has no articles like a, an, or the.

Whether something is definite or indefinite is understood from context:

• В аэропорту я должен сдать багаж.

Depending on context, English might translate this as:

• At the airport, I have to check in the luggage
• At the airport, I have to check in my luggage

Russian does not mark that with articles. Instead, it relies on context, word order, and sometimes extra words like этот, мой, and so on.

Only должен changes:

• male speaker: В аэропорту я должен сдать багаж.
• female speaker: В аэропорту я должна сдать багаж.

That is because должен agrees with the speaker’s gender in the singular.

The rest of the sentence stays the same.