Hún sagði að útborgunin kæmi á föstudag, svo hún gæti borgað reikningana fyrir helgi.

They are subjunctive forms, and that is very common here.

• kæmi = subjunctive form of koma
• gæti = subjunctive form of geta

In this sentence, the speaker is:

1. reporting what someone said, and
2. expressing a purpose/result.

So Icelandic often uses the subjunctive where English would naturally use something like would come and could pay.

Very roughly:

• að útborgunin kæmi = that the payment would come
• svo hún gæti borgað... = so that she could pay...

If you used kemur or getur, it would sound more direct and less like reported/purpose-based wording.

Útborgun is a noun meaning a payout / disbursement / payment out. In context, it often refers to money being paid to someone, such as a wage payment or some other expected payment.

The form útborgunin is:

• definite singular: the payout / the payment
• nominative: because it is the subject of kæmi

So:

• útborgun = a payout
• útborgunin = the payout

Yes. They are closely related.

• borga = to pay
• útborgun = payout / payment out
• borgað = a verb form of borga

That shared borg- part is about paying. So this sentence repeats the same basic idea in two related words:

• the money would be paid out
• so she could pay the bills

That is a nice vocabulary connection to remember.

Because after geta in this kind of construction, Icelandic normally uses borgað.

So the natural pattern is:

• geta borgað = be able to pay
• gæti borgað = could pay

Even though the dictionary form of the verb is borga, the form used here after gæti is borgað. This is normal Icelandic usage.

It is the accusative plural definite form of reikningur.

Breakdown:

• reikningur = bill / invoice / account
• reikninga = bills (plural, indefinite, accusative)
• reikningana = the bills (plural, definite, accusative)

It is in the accusative because it is the direct object of borgað: she could pay the bills.

They introduce two different clauses.

• að = that

  • Hún sagði að... = She said that...

• svo here means so / so that

  • svo hún gæti borgað... = so that she could pay...

A useful point: svo can mean different things in different sentences, including then or so. But here, because of the context and the subjunctive gæti, it is best understood as a purpose clause: so that she could...

Á föstudag is the normal general way to say on Friday.

• á föstudag = on Friday
• á föstudaginn = on the Friday / this specific Friday

So the version without the article is the more neutral, standard time expression. The version with the article would usually sound more specific.

This is similar to many day expressions in Icelandic:

• á mánudag
• á þriðjudag
• á sunnudag

Because fyrir helgi is a very common fixed time expression meaning before the weekend or by the weekend.

Here:

• fyrir = before
• helgi = a case form of helgi (weekend)

Icelandic often leaves out the article in set time phrases like this. So fyrir helgi sounds very natural.

If you said fyrir helgina, that would sound more specifically like before the weekend in question, and in many contexts it is less idiomatic than the simple fyrir helgi.

Probably yes.

The most natural reading is:

• Hún sagði... = She said...
• svo hún gæti... = so that she could...

So both hún forms most likely refer to the same woman.

Grammatically, though, Icelandic does not force that interpretation by itself. If the wider context had two women in it, the second hún could in theory refer to someone else. Usually the surrounding context makes it clear.

Yes. A learner will often see an alternative like:

Hún sagði að útborgunin myndi koma á föstudag...

That also means something like She said that the payment would come on Friday...

The difference is mostly stylistic and grammatical nuance:

• kæmi is a compact subjunctive way to express the reported future-in-the-past idea.
• myndi koma is another very common way to say would come.

Both are useful to recognize. The original sentence is perfectly natural, and kæmi is a form you will meet often in more careful or written Icelandic.

Here is a quick breakdown:

• sagði = past tense of segja (said)
• kæmi = subjunctive of koma (would come / came in reported style)
• gæti = subjunctive of geta (could / would be able to)
• borgað = verb form of borga used after gæti (pay)

So the skeleton of the sentence is:

• Hún sagði ... = She said
• að útborgunin kæmi á föstudag = that the payout would come on Friday
• svo hún gæti borgað reikningana fyrir helgi = so that she could pay the bills before the weekend