Heimahjúkrunin og heimastuðningurinn koma þegar heimilislæknirinn biður um þau.

Because the subject is actually two things joined by og:

• Heimahjúkrunin = the home nursing / home healthcare
• heimastuðningurinn = the home support

Together they make a plural subject, so the verb must also be plural:

• kemur = comes (singular)
• koma = come (plural)

So Heimahjúkrunin og heimastuðningurinn koma means The home nursing and the home support come.

Those endings are the definite article, which in Icelandic is usually attached to the end of the noun rather than written as a separate word.

So:

• heimahjúkrun = home nursing
• heimahjúkrunin = the home nursing

and

• heimastuðningur = home support
• heimastuðningurinn = the home support

Likewise:

• heimilislæknir = family doctor / GP
• heimilislæknirinn = the family doctor / GP

This is one of the most important differences from English.

This is a very common question, because the two nouns have different grammatical genders:

• heimahjúkrunin is feminine
• heimastuðningurinn is masculine

When Icelandic refers back to a mixed group like that, it often uses the neuter plural pronoun:

• þau = they / them (neuter plural)

So biður um þau means asks for them, where them refers to both services together.

This does not mean the services themselves are neuter singular nouns. It means the pronoun referring to the combined pair is neuter plural.

Because the verb here is the expression biðja um, which means to ask for.

So Icelandic says:

• biðja um eitthvað = ask for something
• biðja um þau = ask for them

The preposition um is part of the pattern you need with this meaning. Without um, biðja usually means ask in a different sense, such as asking someone to do something.

For example:

• biðja um hjálp = ask for help
• biðja einhvern = ask someone
• biðja einhvern að... = ask someone to...

It is in the accusative plural, because the preposition um takes the accusative in this kind of usage:

• um þau = for them / about them, depending on context

In this sentence, with biðja um, the meaning is ask for them.

So even if a learner mainly notices þau as a pronoun, it is also useful to learn the pattern:

• biðja um + accusative

Because þegar introduces a subordinate clause meaning when.

In a main clause, Icelandic often has verb-second word order. But in a subordinate clause introduced by a word like þegar, the order is often more straightforward:

• þegar heimilislæknirinn biður um þau
• literally: when the family doctor asks for them

So the subject heimilislæknirinn comes before the verb biður.

This is normal and natural.

Here þegar means when.

So:

• koma þegar heimilislæknirinn biður um þau
• come when the family doctor asks for them

Be careful, because þegar can also mean already in other contexts.

For example:

• Ég er þegar kominn. = I have already arrived.

But in your sentence, because it introduces a clause, it clearly means when.

Biður is the present tense, 3rd person singular, of the verb biðja = to ask / request / pray.

The relevant forms are:

• að biðja = to ask
• ég bið = I ask
• þú biður = you ask
• hann / hún / það biður = he / she / it asks

So:

• heimilislæknirinn biður um þau
• the family doctor asks for them

It is an irregular verb, so the stem changes a bit. That is why learners should memorize it as a verb pattern rather than trying to build it mechanically.

Yes. Icelandic makes very heavy use of compound words.

Here are the parts:

• heima = at home

• hjúkrun = nursing
  → heimahjúkrun = home nursing

• heima = at home

• stuðningur = support
  → heimastuðningur = home support

• heimilis- = of the home / household
• læknir = doctor
  → heimilislæknir = family doctor / GP

So even if the compounds look long, they are often quite logical once you break them into parts.

Because they are built in different ways.

• heima- comes from heima = at home
• heimilis- comes from heimili = home, household, in a genitive-based compound form meaning something like of the home / household

So:

• heimahjúkrun = nursing at home
• heimastuðningur = support at home
• heimilislæknir = doctor of the household / family doctor

You do not always need to analyze every compound deeply, but it is good to notice that Icelandic compounds often reflect old case relationships or adverbial elements.

Because Icelandic normally expresses the by attaching it to the noun as a suffix.

So instead of:

• the doctor

Icelandic usually has:

• læknirinn

Likewise:

• heimilislæknirinn = the family doctor
• heimahjúkrunin = the home nursing
• heimastuðningurinn = the home support

A separate definite word can exist in some contexts, but the suffixed article is the basic pattern learners should expect most of the time.

Yes, depending on the context.

The basic meaning of koma is come, but in sentences about services or people being sent to someone’s home, English may sometimes prefer:

• come
• arrive
• show up
• be provided

So the Icelandic is literally come, but a natural English translation might vary depending on how the service is being described.

No. The main subject of the whole sentence is:

• Heimahjúkrunin og heimastuðningurinn

That is why the main verb is plural:

• koma

Inside the þegar clause, there is a different subject:

• heimilislæknirinn

And its verb is singular:

• biður

So the sentence has two clauses:

1. Heimahjúkrunin og heimastuðningurinn koma
2. þegar heimilislæknirinn biður um þau

It would be:

• Heimahjúkrun og heimastuðningur koma þegar heimilislæknir biður um þau.

That would mean something more like:

• Home nursing and home support come when a family doctor asks for them.

The original sentence with the suffixed article is more specific:

• the home nursing
• the home support
• the family doctor

So the article endings help show whether the meaning is general or specific.

No. Þau can refer to people, things, or a mixed group, depending on the context.

In this sentence it refers to two services, not to people. That is perfectly normal.

What matters is grammatical agreement, not whether the referents are human. Here, þau is the natural plural pronoun for the two items taken together.