Barnen gav farmorn varsin kram innan hon gick hem.

Barnen means the children.

• barn = child / children (the indefinite singular and plural look the same)
• barnet = the child
• barn = children
• barnen = the children

So here -en marks the definite plural.

Because gav is the past tense of ge (to give).

• ge = infinitive, to give
• ger = present tense, gives / are giving
• gav = past tense, gave
• gett = supine/past participle form used in perfect constructions

So Barnen gav farmorn varsin kram means The children gave..., not give or are giving.

Farmorn means the paternal grandmother or the children's grandmother on their father's side.

In Swedish, there is an important difference:

• farmor = father's mother
• mormor = mother's mother

The -n makes it definite:

• farmor = a / grandmother
• farmorn = the grandmother

So Swedish is more specific than English here.

Swedish often puts the indirect object directly after the verb, without a preposition.

So:

• Barnen gav farmorn varsin kram = The children gave their grandmother a hug each

This is very natural Swedish.

You can also say:

• Barnen gav varsin kram till farmorn

That is also understandable, but the version without till is more straightforward and idiomatic here.

Varsin means one each or one apiece.

So varsin kram means that each child gave one hug.

This word is very common in Swedish and does not translate word-for-word into a single English word very neatly.

Examples:

• De fick varsin bok. = They got a book each.
• Vi tog varsin kopp kaffe. = We each had a cup of coffee.

In your sentence, it shows that the hugs were distributed individually: one from each child.

Because varsin is normally used with a singular noun to show that each person gets or gives one of something.

So:

• varsin kram = one hug each

Using a plural noun would usually not fit the meaning here, because the point is exactly one per person.

Also, kram is a common-gender noun, so varsin is the correct form here.

Related forms:

• varsin for common gender singular
• varsitt for neuter singular

For example:

• De fick varsin cykel. = They got a bicycle each.
• Barnen fick varsitt äpple. = The children got an apple each.

Because the sentence means that each child gave one hug.

So Swedish uses:

• varsin kram = a hug each

Even though several hugs happen in total, the noun stays singular because it is understood per child.

This is a clause meaning before she went home.

Breakdown:

• innan = before
• hon = she
• gick = past tense of gå (went)
• hem = home

So:

• innan hon gick hem = before she went home

This is a subordinate clause introduced by innan.

In Swedish, hem often works like an adverb meaning home, so no preposition is needed.

• gå hem = go home
• komma hem = come home
• åka hem = go home / travel home

This is similar to English, where we also usually say go home, not go to home.

So hon gick hem is completely natural.

In this sentence, hon most naturally refers to farmorn.

So the usual reading is:

• The children gave their grandmother a hug each before she went home.

Grammatically, Swedish often relies on context for pronoun reference, just like English. Here, the most logical female person already mentioned is farmorn, so that is the default interpretation.

Yes, it is very normal.

The structure is:

• Barnen = subject
• gav = verb
• farmorn = indirect object
• varsin kram = direct object
• innan hon gick hem = time clause

So Swedish is doing something very similar to English:

• The children gave grandmother a hug each before she went home.

A very literal map would be:

• Barnen = The children
• gav = gave
• farmorn = the grandmother
• varsin kram = one hug each
• innan hon gick hem = before she went home

This word order is standard and natural.

Yes. A few alternatives are possible, depending on style:

• Barnen gav farmorn en kram var innan hon gick hem.
• Barnen gav varsin kram till farmorn innan hon gick hem.

These are understandable, but Barnen gav farmorn varsin kram innan hon gick hem is very idiomatic and compact.

Using varsin is especially elegant in Swedish because it clearly shows one each.