Kan du ställa tillbaka stolen vid bordet?

Because this is a yes/no question.

In Swedish main clauses:

• Du kan ställa tillbaka stolen vid bordet. = You can put the chair back by the table.
• Kan du ställa tillbaka stolen vid bordet? = Can you put the chair back by the table?

So Swedish, like English, often puts the finite verb first in yes/no questions.

In this sentence, it is most naturally understood as a request.

Literally, kan du means can you, so it can ask about ability. But in everyday Swedish it is also a very normal way to ask someone to do something:

• Kan du öppna fönstret? = Can you open the window?
• Kan du hjälpa mig? = Can you help me?

So here it means something like Could you put the chair back by the table?

Ställa is used when you place something so that it is standing upright.

That is why it works well with stolen (the chair). A chair normally stands on its legs, so ställa is the natural verb.

Compare:

• ställa = put/set something standing upright
• lägga = lay/put something down flat
• sätta = set/place something, often in a sitting position or into position

So for a chair, ställa tillbaka sounds more natural than lägga tillbaka.

Tillbaka means back.

In this sentence, it shows that the chair is being returned to its earlier or proper place. So ställa tillbaka means put back or return to its place.

You can think of it much like English put back:

• ställa tillbaka stolen = put the chair back

Yes. It works very much like an English phrasal verb.

The combination ställa tillbaka means more than just place + back word by word; together it gives the idea of putting something back where it belongs.

So it is helpful to learn it as a unit:

• ställa tillbaka = put back
• lägga tillbaka = put back something lying flat
• sätta tillbaka = put back in some other contexts

Because stolen is the definite form: the chair.

Swedish usually adds the definite article to the end of the noun:

• en stol = a chair
• stolen = the chair

Here, the speaker means a specific chair that both people can identify, probably the one that belongs by the table.

Bordet is the definite form of bord:

• ett bord = a table
• bordet = the table

The phrase vid bordet means by the table, next to the table, or sometimes at the table, depending on context.

In this sentence, the idea is that the chair should be placed back in its normal position by/at the table, not on top of it.

Because vid means by, beside, or at.

That fits the relationship between a chair and a table: the chair is normally next to the table.

Compare:

• vid bordet = by/at the table
• på bordet = on the table
• i bordet = in the table (not natural here)

So vid is the correct choice for a chair standing next to a table.

Yes. It can still sound perfectly polite.

Swedish often does not use a direct equivalent of please as often as English does. A sentence like Kan du ställa tillbaka stolen vid bordet? can be polite on its own, especially with a friendly tone.

If you want to make it softer or more polite, you could say things like:

• Kan du vara snäll och ställa tillbaka stolen vid bordet?
• Skulle du kunna ställa tillbaka stolen vid bordet?

But the original sentence is already a normal, polite everyday request.

Yes:

• Kan = can
• du = you
• ställa = put / set upright
• tillbaka = back
• stolen = the chair
• vid = by / at
• bordet = the table

A very literal breakdown is:

Can you set back the chair by the table?

But the most natural English version is:

Can you put the chair back by the table?