Kan du skära en skiva bröd åt barnet?

It can be either, just like English Can you ...?, but in this sentence it is most naturally understood as a request.

So Kan du skära en skiva bröd åt barnet? works like:

• Can you cut a slice of bread for the child?
• or more naturally as a request, Could you cut a slice of bread for the child?

If you really wanted to focus on ability, the context would usually make that clear.

Because skära comes after the modal verb kan.

In Swedish, after modal verbs such as:

• kan = can
• ska = will / going to / supposed to
• måste = must
• vill = want to

you normally use the bare infinitive of the main verb, with no att.

So:

• Kan du skära ...? = Can you cut ...?
• not Kan du skär ...?

Compare:

• Du skär bröd. = You cut / are cutting bread.
• Du kan skära bröd. = You can cut bread.

For the same reason: kan is a modal verb, and Swedish modal verbs are followed directly by the infinitive.

So:

• kan skära
• vill äta
• måste gå

not:

• kan att skära
• vill att äta
• måste att gå

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

Swedish often leaves out of in expressions with measures, amounts, or pieces.

So en skiva bröd literally looks like a slice bread, but it means a slice of bread.

This pattern is very common:

• ett glas vatten = a glass of water
• en kopp kaffe = a cup of coffee
• en bit ost = a piece of cheese
• en skiva bröd = a slice of bread

You do not need av here in normal Swedish.

Yes, often you can.

• en brödskiva = a slice of bread
• en skiva bröd = a slice of bread

The version in your sentence, skära en skiva bröd, emphasizes the act of cutting a slice from some bread.
Brödskiva is the ordinary compound noun for a bread slice as an object.

So both are natural, but the sentence as written is perfectly fine.

Åt often means for, especially when you do something for someone’s benefit.

So here:

• skära en skiva bröd åt barnet = cut a slice of bread for the child

That sounds natural because the action is being done on the child’s behalf.

Till barnet is also possible in some situations, but it often feels more like to the child or intended for the child, rather than emphasizing doing a favor for them.

A useful rough guide:

• åt = for someone, on their behalf
• till = to / for, more directional or recipient-focused

Because barnet is the definite singular form of barn.

• ett barn = a child
• barnet = the child

Barn is an ett-word in Swedish, so the definite ending is -et:

• ett hus → huset
• ett barn → barnet

If the sentence meant for a child, it would be:

• åt ett barn

The sentence follows normal Swedish question word order:

• Kan = finite verb
• du = subject
• skära = infinitive verb
• en skiva bröd = object
• åt barnet = prepositional phrase

So:

Kan du skära en skiva bröd åt barnet?

In yes/no questions, Swedish typically puts the finite verb first, just like English:

• Kan du ...?
• Har du ...?
• Vill du ...?

Compare the statement:

• Du kan skära en skiva bröd åt barnet.

and the question:

• Kan du skära en skiva bröd åt barnet?

Kan du ...? is already a normal and polite way to make a request in Swedish.

Swedish does not use please as automatically or as often as English does. Depending on tone and context, Kan du ...? can be perfectly polite by itself.

If you want to sound softer or warmer, you could add something like:

• snälla = please
• är du snäll och ... = be so kind as to ...

For example:

• Kan du snälla skära en skiva bröd åt barnet?
• Är du snäll och skär en skiva bröd åt barnet?

But the original sentence is completely natural.

A rough pronunciation guide:

• Kan du ≈ kahn du
• skära ≈ SHEH-ra or SHAIR-a as a rough approximation
• en skiva ≈ en skee-va
• bröd has the Swedish ö sound, like German ö or French eu
• åt has a long å, roughly like the vowel in more without the r
• barnet ≈ BAR-net

A few important notes:

• In skära, the sk before ä is not a hard English sk sound. It becomes the Swedish sj-type sound, often approximated by English speakers as sh.
• ö in bröd is a vowel English does not really have, so learners usually need practice with it.
• Stress falls on the first syllable of skära, skiva, bröd, and barnet.