Kan du ge barnet en kaka nu, eller ska hon få glass efter middagen?

Because this is a question.

In Swedish main-clause yes/no questions, the finite verb comes before the subject:

• Du kan ge barnet en kaka. = You can give the child a cookie.
• Kan du ge barnet en kaka? = Can you give the child a cookie?

So kan comes before du to mark it as a question.

It can be either, but here it most likely works like English Can you... ? as a polite suggestion or request.

So Kan du ge barnet en kaka nu...? does not have to mean Are you physically able to do that? It can simply mean:

• Can you give the child a cookie now...?
• Could you give the child a cookie now...?

Barnet is the definite singular form of barn.

• ett barn = a child
• barnet = the child

The noun barn is an ett-word (neuter gender), so its definite singular ending is -et.

Because grammatical gender and natural gender are not the same thing.

• barn is grammatically a neuter noun: ett barn
• But when you refer to an actual child, you normally use a personal pronoun based on the person: hon or han (or sometimes hen)

So:

• barnet = the child
• hon = she

Even though barn is an ett-word, you do not have to keep using a neuter pronoun for a person.

Both are possible.

With ge (to give), Swedish often uses a double-object structure:

• ge barnet en kaka = give the child a cookie

But you can also say:

• ge en kaka till barnet = give a cookie to the child

The first version is very natural and common. The second version is also correct, and can feel a little more explicit because of till.

Because kaka is an en-word.

• en kaka = a cookie / a biscuit / a cake, depending on context
• kakan = the cookie / the cake

Here it is indefinite because it means a cookie, not a specific previously mentioned one.

Få means get or receive.

It often pairs naturally with ge:

• ge någon något = give someone something
• någon får något = someone gets something

So:

• ska hon få glass = should she get ice cream / will she get ice cream

It is the natural Swedish way to express the idea of someone being given something.

Here ska is about what is supposed to happen, what should happen, or what the plan is.

Depending on context, ska hon få glass can mean:

• should she get ice cream
• is she going to get ice cream
• will she get ice cream

So ska does not always mean strict obligation. It often points to a future arrangement, intention, or decision.

Because glass often works as an uncountable noun meaning ice cream in general.

So:

• få glass = get ice cream / get some ice cream

If you want to mean one individual ice cream item, Swedish can use:

• en glass = an ice cream, an ice cream bar/cone/etc.

In this sentence, glass without an article sounds like some ice cream.

Because middagen means the dinner / the meal in this context.

• middag = dinner
• middagen = the dinner / the meal

Swedish often uses the definite form in expressions like this when referring to a specific event or meal in the situation:

• efter middagen = after dinner / after the meal

This is the normal and natural phrasing here.

Yes, nu can move, but its position affects emphasis and style.

Here:

• Kan du ge barnet en kaka nu...?

means now applies naturally to the action give the child a cookie.

You could also say:

• Kan du nu ge barnet en kaka...?
• Nu kan du ge barnet en kaka...

But those feel different in emphasis. The original version is the most neutral and natural for this meaning.

It is one alternative question made of two options joined by eller (or):

• Kan du ge barnet en kaka nu
• eller ska hon få glass efter middagen?

In other words, the speaker is asking which of the two possibilities should happen. That is why the whole sentence ends with one question mark.

Because the second part is also a main-clause question.

Swedish keeps the question word order there too:

• Hon ska få glass efter middagen. = She will/should get ice cream after dinner.
• Ska hon få glass efter middagen? = Should/will she get ice cream after dinner?

After eller, you are getting a second question clause, so ska comes before hon.