Farangurinn hennar kom seint eftir lendinguna, svo hún þurfti að bíða lengi.

The base noun is farangur, meaning luggage / baggage. Icelandic usually adds the definite article to the end of the noun, so:

• farangur = luggage
• farangurinn = the luggage

Here farangurinn is nominative singular, because it is the subject of kom.

Hennar means her and is the genitive/possessive form related to hún. In Icelandic, possessives like hans, hennar, and þeirra are very often placed after the noun:

• farangurinn hennar = her luggage

That word order is completely normal and natural. Putting hennar before the noun would sound much more emphatic or marked.

It is singular. Like English luggage, farangur is often used as a singular collective noun for baggage as a whole, even though it may refer to several bags.

So farangurinn hennar kom means something like her luggage arrived, not necessarily one bag arrived.

Yes. Kom is the past tense of koma, which often means come or arrive. Icelandic commonly uses koma for things like luggage, buses, mail, and so on.

So farangurinn hennar kom seint is a natural way to say that her luggage arrived late.

Because seint is an adverb, not an adjective.

• seinn = late (adjective)
• seint = late (adverb)

Here it modifies the verb kom, telling us how/when the luggage arrived, so the adverb form is needed:

• kom seint = arrived late

A useful pattern is that many Icelandic adverbs look like the neuter singular form of the adjective.

Lendinguna is the definite accusative singular form of lending (landing).

So:

• lending = landing
• lendinguna = the landing

In this sentence, eftir is followed by the accusative, so you get eftir lendinguna. The definite form is used because it refers to a specific landing: the one connected with her trip.

Here svo means so / therefore. It links the first clause to the result in the second clause:

• the luggage arrived late,
• so she had to wait a long time.

In other contexts, svo can also mean things like then or so in other senses, but here it is clearly a result connector.

Hún refers to the female owner of the luggage, not to farangurinn.

That is because farangur is a masculine noun. If the pronoun referred back to farangurinn, you would expect hann, not hún.

So the sentence is saying:

• the luggage arrived late,
• therefore she had to wait.

Because þurfa has an irregular past-tense form:

• infinitive: þurfa = to need / have to
• past: þurfti = had to

So hún þurfti means she had to. This is just a verb form you need to learn as part of the verb’s pattern.

Because þurfa is followed by an infinitive with að:

• þurfa að bíða = have to wait
• þurfa að fara = have to go
• þurfa að vinna = have to work

So hún þurfti að bíða literally means she had to wait.

Also, bíða means to wait. If it has a direct object, it often takes the genitive in Icelandic, but here there is no object stated.

They are both adverbs, but they express different ideas:

• seint = late → tells you when something happened
• lengi = for a long time / long → tells you how long something lasted

So:

• kom seint = arrived late
• bíða lengi = wait a long time

That contrast is very important in Icelandic, just as it is in English.

Not especially. This is normal main-clause word order:

• hún = subject
• þurfti = finite verb

After svo meaning so / therefore, Icelandic can continue with an ordinary main clause. So svo hún þurfti að bíða lengi is a straightforward, natural structure.