Á launaseðlinum sé ég bæði útborgunina og launin mín.

Launaseðlinum is in the dative singular definite.

Here, á means on in the sense of location, not movement. With many Icelandic prepositions, including á, you use:

• dative for a fixed location
• accusative for movement toward/onto something

So:

• á launaseðlinum = on the payslip
• compare with a movement example: á launaseðilinn = onto the payslip

The base noun is launaseðill (payslip), and the definite dative singular form becomes launaseðlinum.

It is a compound noun:

• launa- = from laun (wages, salary)
• seðill = slip, note

So launaseðill literally means something like wage-slip or salary-slip, i.e. payslip.

Then Icelandic adds the definite article as a suffix:

• launaseðill = a payslip
• launaseðillinn = the payslip
• launaseðlinum = on the payslip / to the payslip, depending on context, but here specifically on the payslip because of á with location

Because Icelandic is a verb-second language.

When something other than the subject comes first in the sentence, the finite verb usually comes second. Here the sentence begins with Á launaseðlinum, so the verb sé comes next, and then the subject ég follows.

So:

• Ég sé bæði útborgunina og launin mín. = neutral order
• Á launaseðlinum sé ég bæði útborgunina og launin mín. = with the location fronted

The second version puts more emphasis on where you see these things.

No. Here sé is simply the 1st person singular present tense of the irregular verb sjá (to see).

So:

• ég sé = I see
• þú sérð = you see
• hann/hún/það sér = he/she/it sees

It may look unusual because sjá is irregular, but in this sentence it is just an ordinary present-tense verb form.

It means both ... and ....

In this sentence:

• bæði útborgunina og launin mín = both the payout and my wages

This is a very common Icelandic structure:

• bæði A og B = both A and B

Bæði itself does not change form here.

Útborgunina is the accusative singular definite form of útborgun, a feminine noun.

Breakdown:

• útborgun = payout, amount paid out
• útborgunin = the payout (nominative)
• útborgunina = the payout (accusative)

It is in the accusative because sjá (to see) normally takes a direct object in the accusative.

So ég sé útborgunina means I see the payout.

Yes, it can correspond to English salary or wages, but Icelandic laun is normally a plural noun.

So even when English uses a singular idea like salary, Icelandic often uses plural grammar:

• laun = wages / salary
• launin = the wages / the salary

This is very common and natural in Icelandic. So a learner should think of laun as a word that is usually treated as plural.

In Icelandic, when a noun is definite, the possessive pronoun is very often placed after the noun:

• launin mín = my wages
• bíllinn minn = my car
• bókin mín = my book

This is the most natural everyday pattern.

Putting the possessive first, as in mín laun, is possible in some contexts, but it often sounds more emphatic, contrastive, or stylistically marked. For a normal sentence like this, launin mín is the expected form.

It is the accusative plural, because it is also a direct object of sjá.

However, with laun, the nominative and accusative plural forms look the same:

• launin can be nominative plural definite
• launin can also be accusative plural definite

The possessive mín agrees with launin in gender, number, and case. Here it is the form used with neuter plural nominative/accusative.

So even though the case is accusative in this sentence, the form does not visibly change.

Yes, in ordinary usage sjá takes its direct object in the accusative.

That is why both objects in this sentence are accusative:

• útborgunina
• launin mín

So the structure is:

• sé = verb
• ég = subject
• útborgunina and launin mín = direct objects

They are related, but not the same thing.

• laun refers to your wages/salary
• útborgun refers to the amount actually paid out

On a payslip, this distinction matters. Your laun may refer to your pay more generally, while útborgun often refers to the final amount that reaches you after deductions such as tax or other payments.

So the sentence is saying that on the payslip, the speaker can see both the payout amount and their wages.

Yes. That sentence is also correct and natural.

The difference is mainly focus:

• Ég sé bæði útborgunina og launin mín á launaseðlinum.
  More neutral: I see both the payout and my wages on the payslip.

• Á launaseðlinum sé ég bæði útborgunina og launin mín.
  Emphasizes where you see them: On the payslip, I see both...

So the original version is not strange; it just gives extra prominence to Á launaseðlinum.