Ef afhendingin kemur of seint í ágúst, þarf sendandinn að hringja aftur.

Because Icelandic follows a verb-second pattern in main clauses.

When the sentence starts with the subordinate clause Ef afhendingin kemur of seint í ágúst, that whole clause takes the first slot. In the main clause, the finite verb must then come second, so you get:

þarf sendandinn að hringja aftur

If you put the main clause first by itself, the more basic order would be:

Sendandinn þarf að hringja aftur.

So this is not random inversion; it is a normal Icelandic word-order rule.

Those endings are the suffixed definite article in Icelandic.

• afhending = delivery

• afhendingin = the delivery

• sendandi = sender
• sendandinn = the sender

Unlike English, Icelandic usually puts the onto the end of the noun rather than using a separate word.

Icelandic often uses the present tense for future meaning when the context already makes the time clear.

Here, the condition introduced by ef and the time phrase í ágúst make it clear that this is about a future possibility. So:

• kemur = comes / arrives
• þarf = needs to / must

This is very natural in Icelandic, just as English can say things like If he comes tomorrow, I call him in some informal or planned contexts, though English uses this less freely.

Because seint is functioning as an adverb here.

The phrase means arrives too late, so seint describes how the delivery comes. It modifies the verb kemur.

• seinn / sein / seint can be an adjective meaning late
• seint is also the adverb form meaning late

Compare:

• Afhendingin kemur of seint. = The delivery arrives too late.
• Afhendingin er of sein. = The delivery is too late.

In the second sentence, sein is feminine because afhending is feminine.

Of means too in the sense of excessively.

So:

• of seint = too late
• of mikið = too much
• of hratt = too quickly

It is a very common word in Icelandic.

Because í is the normal preposition for months when you mean in August, in May, and so on.

So:

• í ágúst = in August
• í janúar = in January

A useful extra note: month names are normally not capitalized in Icelandic, so ágúst is correctly written with a lowercase letter unless it starts the sentence.

Here að is the infinitive marker, like English to.

• hringja = call / ring
• að hringja = to call

After þurfa (to need / to have to), Icelandic normally uses að + infinitive:

• þarf að hringja = needs to call / must call

Yes. Although koma basically means come, it is often used where English would naturally say arrive.

So in this sentence:

• afhendingin kemur seint = the delivery arrives late

This is very normal Icelandic usage, especially for things like deliveries, mail, buses, and shipments.

Here aftur means again.

So:

• að hringja aftur = to call again / call back

Its position is normal. Icelandic adverbs are fairly flexible, but putting aftur at the end is very common and natural here.

Depending on context, aftur can also mean back, but in this sentence again is the natural reading.

Two important Icelandic letters appear here:

• þ is pronounced like th in thin
• ð is pronounced roughly like th in this, though it can sound very soft

So:

• þarf starts with the thin sound
• að has a soft ð, and in fast speech it may sound quite light

Also, accented vowels like á are different vowels, not just stressed versions of plain vowels. In ágúst, á has its own distinct sound.

Yes. A very natural alternative is:

Sendandinn þarf að hringja aftur ef afhendingin kemur of seint í ágúst.

That may feel easier to an English speaker because the main clause starts in the usual order:

Sendandinn þarf ...

The original sentence is also completely normal; it just shows the common Icelandic effect of putting the verb first in the main clause after an opening ef clause.