Kan du lägga en servett bredvid tallriken och ställa kannan på bordet?

Here Kan du ... ? is usually a request, not a literal question about ability.

So the sentence is functioning like:

• Can you ... ?
• Could you ... ?

In everyday Swedish, Kan du ... ? is a very normal and polite way to ask someone to do something. It does not usually sound like you are doubting whether they are physically able to do it.

Because this is a yes/no question.

In Swedish, yes/no questions normally put the finite verb first:

• Kan du lägga ... ? = Can you put ... ?

Compare that with a statement:

• Du kan lägga ... = You can put ...

So the order changes depending on whether you are asking or stating.

Because kan is a modal verb, and modal verbs in Swedish are followed by the infinitive without att.

So you say:

• kan lägga
• kan ställa

not:

• kan att lägga
• kan att ställa

This is similar to English, where we say can put, not can to put.

Other common Swedish modal verbs work the same way, for example:

• vill gå = want to go
• måste läsa = must read
• ska göra = will / going to do

Swedish often chooses different placement verbs depending on the object's position.

• lägga = lay / put down something that ends up lying flat
• ställa = stand / set down something that ends up standing upright

In this sentence:

• en servett is something you typically lay down → lägga en servett
• kannan is something that normally stands upright → ställa kannan

English often uses put for both, but Swedish is more specific here.

You may also later meet:

• sätta for something placed in a sitting position
• hänga for something hung up

Because the sentence is talking about:

• a napkin → any one napkin, not a specific one already identified
• the plate, the jug/pitcher, the table → specific things that are understood from the situation

So:

• en servett = a napkin
• tallriken = the plate
• kannan = the jug/pitcher
• bordet = the table

This is very natural if the speaker and listener both know which plate, jug, and table are meant.

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

Examples from this sentence:

• en tallrik → tallriken = the plate
• en kanna → kannan = the jug/pitcher
• ett bord → bordet = the table

So instead of putting a separate word before the noun like English the, Swedish often adds an ending.

Very roughly:

• many en-words take -en
• many ett-words take -et

That is why you see:

• kannan
• tallriken
• bordet

Because servett is an en-word in Swedish:

• en servett
• servetten

Grammatical gender in Swedish has to be learned noun by noun. There is not always a reliable rule from the meaning alone.

So for vocabulary learning, it is best to memorize nouns with their article:

• en servett
• en tallrik
• en kanna
• ett bord

Bredvid means beside or next to.

In the sentence:

• bredvid tallriken = next to the plate

It is a very common way to describe location.

Examples:

• Stolen står bredvid bordet. = The chair is next to the table.
• Lägg boken bredvid lampan. = Put the book next to the lamp.

So lägga en servett bredvid tallriken means to place the napkin in a position next to the plate.

Because på is used for something located on a surface.

A table is treated as a surface, so:

• på bordet = on the table

Compare:

• på golvet = on the floor
• på stolen = on the chair

If something is inside something enclosed, Swedish often uses i instead:

• i lådan = in the box
• i rummet = in the room

So here på bordet is exactly what you would expect.

Because both verbs are part of the same request.

The structure is:

• Kan du lägga ... och ställa ... ?

That means:

• Can you put ... and place ... ?

The subject du and the modal verb kan apply to both infinitives:

• lägga
• ställa

You could think of it as:

• Can you [put a napkin next to the plate] and [set the jug on the table]?

Repeating kan du would be unnecessary unless you wanted extra emphasis.

Not always exactly. Kanna can mean different container words in English depending on context, such as:

• jug
• pitcher
• sometimes pot

In this sentence, jug or pitcher is probably the most natural translation if it is something being placed on a table.

So kannan means the jug/pitcher here.

Yes, it is natural.

It sounds like a normal everyday request. A Swede might also say slightly different versions depending on tone and context, for example:

• Kan du lägga en servett bredvid tallriken och ställa kannan på bordet?
• Kan du ställa kannan på bordet och lägga en servett bredvid tallriken?
• Skulle du kunna lägga en servett bredvid tallriken och ställa kannan på bordet?
  This sounds a bit more formal or extra polite.

But the original sentence is completely normal and idiomatic.

A useful way to see it is:

• Kan = finite verb
• du = subject
• lägga = infinitive
• en servett = object
• bredvid tallriken = place expression
• och ställa = second infinitive, linked with and
• kannan = object
• på bordet = place expression

So each mini-part follows a very common pattern:

• verb + object + place

That makes the sentence easy to build once you know the words.