Kan du bära ner kartongen till källaren?

Because Swedish yes/no questions usually use verb-first word order.

• Du kan bära ner kartongen till källaren. = a statement
• Kan du bära ner kartongen till källaren? = a question/request

So this is the normal Swedish way to say Can you ...?

It can be both, just like English Can you ...?

In real life, Kan du bära ner kartongen till källaren? will often be understood as a request, not just a question about physical ability.

If you want to sound more polite or softer, Swedish can also use:

• Kan du vara snäll och bära ner kartongen till källaren?
• Skulle du kunna bära ner kartongen till källaren?

But Kan du ...? is already very common and natural.

Because kan is a modal verb, and after modal verbs Swedish normally uses the infinitive without att.

So:

• kan bära
• ska bära
• vill bära
• måste bära

Not kan bär.

This is similar to English:

• can carry
• not can carries

Ner means down, especially movement to a lower place.

So bära ner means carry down.

It is acting like a particle connected to the verb:

• bära upp = carry up
• bära in = carry in
• bära ut = carry out
• bära ner = carry down

In this sentence, it fits naturally because the destination is the basement, which is lower down.

Both ner and ned exist, and in many cases they are just different forms of the same word.

• ner is very common in everyday spoken and written Swedish
• ned can sound a bit more formal or traditional in some contexts

So bära ner and bära ned are both possible. For many learners, ner is the most useful everyday form to recognize first.

Because kartongen is the definite form: the box / the cardboard box.

Swedish usually puts the definite article at the end of the noun:

• en kartong = a box / a carton
• kartongen = the box / the carton

So the -en ending works like English the.

For the same reason: källaren is the definite form of källare.

• en källare = a basement / a cellar
• källaren = the basement / the cellar

In this sentence, it is probably a specific basement already known from the situation, such as the basement in the house or building.

Because till shows movement toward a destination: to the basement.

Compare:

• bära ner kartongen till källaren = carry the box to the basement
• kartongen står i källaren = the box is in the basement

So:

• till = direction / destination
• i = location

This is a very important difference in Swedish.

Modern Swedish normally uses du with almost everyone, even in many polite situations.

So Kan du ...? is not automatically rude or too informal. It is standard everyday Swedish.

There is also ni, but it is much less central than formal you in some other European languages. A learner should generally treat du as the normal default.

Yes, sometimes ta ner kartongen till källaren could also work, but bära is more specific.

• bära = carry, physically support while moving it
• ta = take, bring, move; broader and less specific

So bära is a good choice when the idea is literally carrying the box downstairs.

Yes, it is very close in meaning. In many contexts, källare can be translated as either basement or cellar.

In everyday Swedish, källare is the normal word you will often see for the lower part of a building. In English, whether you choose basement or cellar depends more on the style and situation.