Ég á eftir að senda henni skilaboð þegar ég kem á staðinn.

In this sentence, á is part of the fixed expression eiga eftir að + infinitive.

So ég á eftir að senda does not mean I own after to send. It means something like:

• I still have to send
• I have yet to send
• I’m going to send later

The idea is that the action remains undone at the moment of speaking.

Að eiga eftir að + verb expresses that something is still left to do.

So:

• Ég á eftir að senda henni skilaboð = I still have to / I have yet to send her a message
• In context, it often sounds very natural as I’ll send her a message

It is not just a neutral future. It suggests that the action has not happened yet, but is expected to happen later.

Not exactly.

• ætla að = intend to / plan to
• munu = a more direct will, often more formal, predictive, or written
• eiga eftir að = still have left to do / have yet to do

So the nuance is different:

• Ég ætla að senda henni skilaboð = I intend to send her a message.
• Ég mun senda henni skilaboð = I will send her a message.
• Ég á eftir að senda henni skilaboð = I still haven’t sent her a message, but that is still to come.

Icelandic often does not need a special future tense marker. Future meaning is very often shown by:

• context
• the present tense
• a construction like eiga eftir að
• time expressions such as þegar

So even without a separate word meaning will, the sentence clearly refers to a future action.

This is actually similar to English in phrases like I’ll text her when I get there, where get is present in form but refers to the future.

Because Icelandic commonly uses the present tense after time words like þegar when talking about the future.

So:

• þegar ég kem á staðinn = when I get there / when I arrive

This is very similar to English, where we normally say:

• when I get there not
• when I will get there

So kem is present tense in form, but future in meaning because of the time clause.

Henni is the dative form of hún.

It is used because að senda often takes this pattern:

• senda e-m e-ð = send someone something

So:

• henni = to her (indirect object, dative)
• skilaboð = message/message(s) (direct object)

A very common Icelandic pattern is:

• Ég sendi henni skilaboð = I sent her a message.
• Hann sendi mér bréf = He sent me a letter.

Yes, skilaboð is plural in form, but Icelandic often uses it where English would simply say a message.

So:

• senda henni skilaboð can mean send her a message
• depending on context, it can also mean send her messages

Also, Icelandic has no separate indefinite article like English a/an, so a bare noun often covers what English would express with a.

So the combination of:

• no a
• a plural-looking noun

can feel strange to English speakers at first, but it is normal Icelandic usage.

Á staðinn means something like:

• to the place
• to the location
• more naturally here, there or to the scene/on site

In this sentence, þegar ég kem á staðinn is best understood as:

• when I get there
• when I arrive on site

It is a very common expression.

This is a case difference caused by motion vs. location.

With á:

• accusative is often used for motion toward a place
• dative is often used for being at a place

So:

• á staðinn = to the place / there → movement
• á staðnum = at the place / on the spot → location

In your sentence, the speaker is arriving somewhere, so movement is involved, and that is why staðinn is used.

Because þegar ég kem á staðinn is a subordinate clause.

In Icelandic, normal word order inside a subordinate clause is typically:

• conjunction + subject + verb

So:

• þegar ég kem = correct

Icelandic verb-second word order mainly applies to main clauses, not subordinate clauses like this one.

Compare:

• Ég sendi henni skilaboð þegar ég kem á staðinn.
• Þegar ég kem á staðinn, sendi ég henni skilaboð.

Notice that when the þegar-clause comes first, the following main clause shows inversion: sendi ég.

You could, but senda henni skilaboð is the more normal and direct way.

The usual pattern is:

• senda e-m skilaboð = send someone a message

Using til hennar is possible in some contexts, but it is less basic and often sounds more explicit or less idiomatic here.

So for a learner, the safest and most natural version is:

• senda henni skilaboð

No. Þegar can also mean already in other contexts.

For example:

• Ég er þegar kominn = I have already arrived

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

• þegar ég kem á staðinn = when I get there

So the meaning depends on how it is used in the sentence.