Hún segir að hún vilji tjalda aftur á hálendinu, þó að veðrið breytist hratt þar.

Vilji is the present subjunctive of vilja (to want).
Vill is the present indicative.

In this sentence, að hún vilji tjalda... is a clause of indirect/reported speech after segir (says). In Icelandic, that kind of clause often takes the subjunctive, especially in more careful or standard language.

So:

• hún vill = she wants
• hún segir að hún vilji = she says that she wants

A good way to think of it is: the speaker is reporting her statement, not directly asserting the desire as a plain fact.

Because the verb here is breytast, not breyta.

• breyta usually means to change something / alter something
• breytast means to change / become different

So:

• Hún breytir planinu = She changes the plan
• Veðrið breytist = The weather changes

In this sentence, the weather is changing by itself, so Icelandic uses breytast.

Also, after þó að (although / even though), the subjunctive is normally used. With breytast, the 3rd person singular present form breytist looks the same in both indicative and subjunctive, so the mood is understood from the grammar, not from a visibly different ending.

They do two different jobs.

1. segir að ...
   Here að means that and introduces a subordinate clause:

   • Hún segir að... = She says that...

2. þó að ...
   Here að is part of the fixed conjunction þó að, which means although / even though.

So even though the same word appears twice, it is not the same structure both times.

Hálendinu is dative singular definite of hálendi (highland / the Highlands).

The preposition á can take different cases depending on meaning:

• accusative for motion toward a place
• dative for location in/at/on a place

Here the meaning is location: she wants to camp on/in the highlands, not move onto them at that moment. So Icelandic uses dative:

• á hálendinu = in/on the Highlands

Compare the general pattern:

• fara á staðinn = go to the place
• vera á staðnum = be at the place

Very often, yes.

In Icelandic, hálendið commonly refers to the Icelandic Highlands, especially the inland highland region. So a native speaker may naturally hear á hálendinu as in the Icelandic Highlands, not just any highlands in general.

Context decides, but the definite form strongly fits that interpretation.

Veðrið means the weather.

Icelandic often uses the definite form when talking about the weather in a specific situation or place, just like English usually says the weather rather than simply weather in this kind of sentence.

So:

• veður = weather in a more general sense
• veðrið = the weather

Here it means the weather there / the weather in that area.

Because Icelandic subordinate clauses still need an explicit subject.

So after að, you normally say:

• að hún vilji... = that she wants...

You cannot usually drop the subject the way a learner might be tempted to.

The repetition is completely normal:

• Hún segir að hún vilji...

English does the same:

• She says that she wants...

not

• She says that wants...

Because Icelandic verb-second order is mainly a main-clause pattern.

In the main clause:

• Hún segir...

That is normal.

But in subordinate clauses introduced by words like að and þó að, Icelandic usually has more straightforward clause order:

• að hún vilji...
• þó að veðrið breytist...

So the conjunction comes first, then the subject, then the verb. Learners often notice that Icelandic main clauses feel more like Germanic V2, while subordinate clauses are less so.

Tjalda means to camp in a tent or more literally to pitch a tent.

So this sentence is specifically about tent-camping, not just staying outdoors in a broad sense.

That is useful because English camp can be a bit wider:

• tent camping
• camper-van camping
• campsite staying in general

But tjalda points more specifically to the idea of a tent.

Here aftur most naturally means again or once more.

So the idea is that she wants to camp in the Highlands again.

Aftur can also mean back in some contexts, but in this sentence again is the most natural reading.

Its position is also normal:

• vilji tjalda aftur á hálendinu

A common Icelandic adverb order is:

• verb
• adverb
• place phrase

So tjalda aftur á hálendinu sounds very natural.

Because þar means there, and it refers back to the Highlands.

So:

• á hálendinu = in the Highlands
• þar = there

Icelandic often repeats location this way when the second clause comments on that place:

• ... á hálendinu, þó að veðrið breytist hratt þar.

It makes the connection explicit: the weather changes quickly there, in that place.

English can do the same:

• ... in the Highlands, although the weather changes quickly there.

Yes. Þó að and þótt are very close in meaning, and both can mean although / even though.

So this sentence could also be written as:

• Hún segir að hún vilji tjalda aftur á hálendinu, þótt veðrið breytist hratt þar.

That would be perfectly natural.

In both patterns, the subjunctive is normally expected in the subordinate clause.