Þær senda hvor annarri skilaboð þegar ein þeirra kemur seint.

Þær is the nominative plural feminine form of they.

So this tells you that the subject is:

• plural: more than one person
• feminine: an all-female group, or a group of nouns that are grammatically feminine

English just says they, but Icelandic keeps the gender distinction:

• þeir = they (masculine / mixed group)
• þær = they (feminine)
• þau = they (neuter)

In this sentence, þær is the subject of senda.

Hvor annarri is the Icelandic reciprocal expression meaning each other.

Icelandic does not normally use a single word for this idea. Instead, it uses a two-part expression based on hvor and annar.

In this sentence:

• þær senda hvor annarri skilaboð
• literally: they send to each other messages

A useful thing to notice is that even though the subject is plural, the reciprocal expression is built around the idea of one person in relation to another person, so it appears in singular forms.

Because the verb senda takes:

• the recipient in the dative
• the thing sent in the accusative

So the pattern is:

• að senda einhverjum eitthvað
• to send someone something

Here:

• hvor annarri = to each other → recipient, so dative
• skilaboð = messages → thing sent, so accusative

That is why you get annarri, the dative singular feminine form.

Skilaboð is a noun that is very often used in a plural form in Icelandic, even when English might say a message or messages.

So:

• skilaboð = message / messages, depending on context

In this sentence it is the direct object of senda, so it is in the accusative. For this noun, the form skilaboð is the same in nominative and accusative plural.

This is a very common word to learn as a kind of set expression:

• senda skilaboð = send a message / send messages

Because ein must agree with the person being referred to, and here that person is understood as feminine singular.

Since the subject group is þær, one member of that group is:

• ein = one (feminine) not
• einn = masculine
• eitt = neuter

So:

• ein þeirra = one of them (female)

Because Icelandic uses the genitive plural after expressions like one of them.

So:

• ein þeirra = literally one of them
• þeirra is the genitive plural form of þær

This is a very common pattern:

• einn þeirra = one of them (masculine/mixed)
• ein þeirra = one of them (feminine)
• eitt þeirra = one of them (neuter)

You can think of it as a partitive genitive: one member out of a larger group.

Because kemur belongs to the subordinate clause, and its subject is not þær. Its subject is ein þeirra.

So the structure is:

• Main clause: Þær senda hvor annarri skilaboð
• Subordinate clause: þegar ein þeirra kemur seint

Inside the þegar clause, the subject is:

• ein þeirra = one of them

That is singular, so the verb must also be singular:

• ein þeirra kemur
• not ein þeirra koma

Because seint is an adverb, and it describes how someone comes: late.

Compare:

• seinn / sein / seint = the adjective late
• seint = also the adverb form late

Here it modifies the verb kemur:

• kemur seint = arrives late / comes late

So Icelandic needs the adverb, just as English does in comes late.

It can be understood as either, depending on context, but in a sentence like this with the present tense, it often has a habitual sense:

• when
• or more naturally in English, whenever

So the sentence can describe a repeated situation:

• whenever one of them is late, they send each other messages

That habitual reading is very natural here.

Yes. You can say:

• Þegar ein þeirra kemur seint, senda þær hvor annarri skilaboð.

That is perfectly normal Icelandic.

The important thing is the word order in the main clause. When the subordinate clause comes first, the finite verb in the main clause still comes early, so you get:

• Þegar ... , senda þær ... not
• Þegar ... , þær senda ...

That is a standard Icelandic word-order pattern.

Yes. The present tense here is very natural for a habitual or repeated action.

So:

• Þær senda ... þegar ein þeirra kemur seint means something like
• They send each other messages when/whenever one of them is late

If you wanted to describe one specific past situation, Icelandic would normally switch to past-tense forms instead.