Jag och Sara tog varsin mugg te, men barnen ville hellre ha glass.

Varsin means one each or each their own.

So Jag och Sara tog varsin mugg te means that there were two people, and each person had one mug of tea.

A useful way to think of it is:

• en mugg te = one mug of tea
• varsin mugg te = one mug of tea each

Swedish uses varsin when several people each get one item.

Examples:

• De fick varsitt äpple = They got an apple each
• Vi hade varsin cykel = We each had a bicycle

Because varsin is used with a singular noun when each person gets one of something.

So:

• varsin mugg = one mug each

If each person had more than one, Swedish could use varsina with a plural noun:

• De hade varsina böcker = They each had their own books / sets of books

In your sentence, each person has just one mug, so singular mugg is correct.

Because varsin already includes the idea of one each. Adding en would be incorrect in standard Swedish.

So you say:

• varsin mugg not
• en varsin mugg

This is a very common learner question, because English often uses a in similar phrases, but Swedish does not here.

In Swedish, container words are often followed directly by the thing inside them, with no preposition.

So these are natural:

• en kopp kaffe = a cup of coffee
• ett glas vatten = a glass of water
• en mugg te = a mug of tea

You can sometimes say med in other contexts, but it changes the feel slightly:

• en mugg med te = a mug with tea in it

That version focuses a bit more on the mug as an object containing tea. In ordinary everyday language, en mugg te is the most natural way to say it.

Because te and glass are being used as uncountable or general food/drink nouns here.

In Swedish, after a container noun, you normally just say:

• en kopp kaffe
• ett glas mjölk
• en mugg te

And after ha in a food context, you can also say:

• ha glass
• ha kaffe
• ha te

This works much like English in phrases such as have tea or eat ice cream, where you also often do not need an article.

Yes, tog is the past tense of ta, which usually means take. But in Swedish, ta is also often used in food and drink contexts to mean something like:

• have
• take
• choose
• order

So Jag och Sara tog varsin mugg te means that they had or took a mug of tea each.

This is very natural Swedish. Similar examples:

• Jag tar kaffe = I’ll have coffee
• Hon tog sallad = She had / chose salad

So even though took may sound strange in English, it is normal in Swedish.

Because ville is the past tense of vilja, meaning to want, and it is followed by the infinitive ha.

So:

• ville ha = wanted to have / wanted

This is a very common Swedish structure:

• Jag vill ha kaffe = I want coffee
• De ville ha glass = They wanted ice cream

In English, we often just say wanted ice cream, but Swedish commonly uses vilja ha.

Also, after vilja, you do not use att here:

• ville ha not
• ville att ha

Hellre means rather.

So barnen ville hellre ha glass means the children would rather have ice cream.

As for position: in a main clause, Swedish adverbs like hellre often come after the finite verb.

Here:

• ville = finite verb
• hellre = adverb
• ha = infinitive

So the pattern is:

• barnen ville hellre ha glass

This word order is very typical in Swedish.

Compare:

• Jag vill hellre stanna hemma = I would rather stay home
• Hon köpte hellre te än kaffe = She preferred to buy tea rather than coffee

Barnen is the definite plural form, meaning the children.

The basic noun is:

• ett barn = a child
• barn = children
• barnen = the children

In this sentence, we are talking about a specific group of children, so the definite form barnen is used.

This is very common in Swedish: plural definite nouns often end in -na or -en, depending on the word.

Yes, glass in Swedish can mean ice cream, and that is one of the first things English speakers usually notice.

So:

• glass = ice cream
• glas = glass, or a drinking glass

Notice the difference:

• glass with double s = ice cream
• glas with one s = glass / a glass

So in your sentence, barnen ville hellre ha glass, it definitely means ice cream.

Yes, Sara och jag is also possible.

Both are understandable and natural in Swedish, but there can be a difference in style:

• Jag och Sara is very common in everyday spoken Swedish
• Sara och jag may sound a bit more careful or polite to some speakers

Unlike the strict school rule in English about Sara and I, Swedish is often less strict about this kind of ordering in casual speech.

So Jag och Sara is perfectly normal here.

Yes.

They come from these infinitives:

• ta → tog = take → took
• vilja → ville = want → wanted

Both are irregular and very common, so they are worth memorizing early.

A few useful forms:

• ta / tog / tagit
• vilja / ville / velat

Since these verbs are so common, learners will see them all the time in everyday Swedish.