Við ætluðum að hittast á kaffihúsi til að sættast, en hún þurfti að vinna lengur.

Ætluðum is the 1st person plural past tense of að ætla.

So:

• ég ætla = I intend / I am going to
• við ætlum = we intend / we are going to
• við ætluðum = we intended / we were going to

In this sentence, við ætluðum að hittast means we were going to meet or we had planned to meet.

The ending -ðum is a very common past-tense ending for we in Icelandic verbs.

Here, að is the infinitive marker, similar to English to.

So:

• ætla að gera eitthvað = to intend to do something
• við ætluðum að hittast = we intended to meet

This is a very common pattern in Icelandic:

• hann vill að fara? No
• hann vill fara = he wants to go
  because not all verbs take að
• but:
• hún ætlar að koma = she intends to come
• við þurftum að vinna = we had to work

So after ætla, you normally use að + infinitive.

Hittast means to meet each other or to meet up.

The -st ending is very important in Icelandic. It often creates a middle/reflexive/reciprocal meaning. In this case, it gives the sense that the action is mutual:

• hitta = meet, find, hit depending on context
• hittast = meet each other / get together

So:

• Við hittum hana = We meet her / We met her
• Við hittumst = We meet each other / We met

In your sentence, að hittast is the natural form because the subject is plural (we) and the meaning is mutual.

Icelandic often uses á with many public places or institutions where English might use in or at.

So á kaffihúsi means at a café / in a café, but the Icelandic preposition is á.

This is similar to other common expressions:

• á veitingastað = at a restaurant
• á bar = at a bar
• á skrifstofu = at an office
• á spítala = in hospital / at the hospital

The choice of preposition is something you often just have to learn with the noun.

Also, because this is a location meaning, á takes the dative case, which is why you see kaffihúsi.

Kaffihúsi is the dative singular form of kaffihús.

The preposition á can take either:

• accusative for movement toward something
• dative for location

Here the meaning is static location: they were going to meet at a café, not go onto/into one as a direction. So Icelandic uses the dative:

• á kaffihúsi = at a café

This is a very common pattern:

• á borði = on a table
• á Íslandi = in Iceland
• á kaffihúsi = at a café

Til að means to or in order to when expressing purpose.

So:

• til að sættast = to make up / in order to reconcile

This is different from the earlier að in ætluðum að hittast.

Compare the two:

• ætluðum að hittast = we intended to meet
  (að introduces the infinitive after ætla)
• til að sættast = in order to make up
  (til að expresses purpose)

A helpful way to think about it:

• að + verb after another verb often just means to do
• til að + verb often means in order to do

Sættast means to reconcile, to make up, or to become friends again after an argument.

It comes from the idea of becoming sáttur/sátt = reconciled, in agreement, at peace.

Like hittast, it has the -st ending, which again gives a middle/reciprocal sense. So sættast often means that two people become reconciled with each other.

Examples:

• Þau sættust. = They made up.
• Við þurfum að sættast. = We need to reconcile.

In your sentence, til að sættast tells us the purpose of the meeting: they were going to meet at a café to make up.

Because þurfa also commonly takes að + infinitive.

So:

• þurfa að vinna = have to work
• þurfti að vinna = had to work

This is another very common Icelandic verb pattern:

• Ég þarf að fara. = I need to go.
• Hún þurfti að vinna. = She had to work.

So both ætla and þurfa are verbs that are commonly followed by að + infinitive.

Þurfti is the past tense singular of að þurfa = to need / to have to.

In this sentence:

• hún þurfti að vinna = she had to work

Compare:

• ég þarf = I need / I have to
• hún þarf = she needs / has to
• hún þurfti = she needed / had to

So the sentence moves from the past plan (við ætluðum) to the reason it did not happen (hún þurfti að vinna lengur).

Here, lengur means longer.

So:

• hún þurfti að vinna lengur = she had to work longer

It is the comparative form related to langur = long.

A useful note: lengur is also often used in negative sentences to mean any longer / anymore:

• Ég bý þar ekki lengur. = I don’t live there anymore.

But in your sentence it simply means for a longer time.

Yes. In this sentence, en means but.

So the structure is:

• Við ætluðum að hittast ... = We were going to meet ...
• en hún þurfti að vinna lengur. = but she had to work longer.

It connects two clauses in contrast, just like English but.

Yes, that is the natural implication.

The first clause says:

• Við ætluðum að hittast = We were going to meet / We had planned to meet

The second clause gives a reason that interfered with that plan:

• en hún þurfti að vinna lengur = but she had to work longer

So the most likely interpretation is that the planned meeting either:

• did not happen at all, or
• was delayed/cancelled

The sentence does not explicitly say we didn’t meet, but that is strongly suggested.

No, it is not a coincidence. The -st form is very common in Icelandic and often expresses meanings like:

• reflexive
• middle voice
• reciprocal
• something happening to or among the subject

In this sentence, both verbs naturally involve a mutual relationship between people:

• hittast = meet each other
• sættast = reconcile / make up with each other

So the -st form fits both meanings very well.

For learners, it is helpful to notice that many everyday Icelandic verbs appear in these -st forms, and they often do not translate word-for-word into English reflexives.

Both are possible, depending on how natural you want the English to sound.

Literally and grammatically, til að expresses purpose, so in order to make up is very accurate.

But in natural English, you would often simply say:

• We were going to meet at a café to make up

So:

• til að sættast = to make up
• more explicitly: in order to make up

Both capture the Icelandic meaning well.