Ég sit á svölunum í sólskininu.

Because sit is the correct 1st person singular present-tense form of sitja (to sit).

A quick comparison:

• ég sit = I sit / I am sitting
• þú situr = you sit / are sitting
• hann/hún/það situr = he/she/it sits / is sitting

So situr is used with you/he/she/it, not with I.

It can mean either, depending on context. In this sentence, it most naturally means I am sitting.

Icelandic often uses the simple present where English prefers the present continuous. So:

• Ég sit á svölunum very naturally means I am sitting on the balcony.

You can also hear ég er að sitja, but with posture verbs like sitja it is very common just to use the simple present.

Because svalir is a noun that is normally used in the plural in Icelandic, even when English uses the singular balcony.

So:

• svalir = balcony / balconies
• á svölunum = on the balcony

This is one of those places where Icelandic and English divide things differently. English has some similar ideas with words like stairs or pants, which are plural in form even when referring to one thing.

Because Icelandic uses á with svalir.

Here, á means on or sometimes more generally on/at depending on the place. With balconies, terraces, islands, streets, and some other locations, Icelandic often uses prepositions differently from English.

So the natural phrase is:

• á svölunum = on the balcony

Even if English and Icelandic both use on here, it is still best to learn it as the normal Icelandic pattern: á svölunum.

Because í is the natural preposition for being in sunshine/sunlight, and sólskininu is the dative singular definite form of sólskin (sunshine).

So:

• í sólskini = in sunshine / in sunlight
• í sólskininu = in the sunshine

This sounds very natural in Icelandic.

Those endings show two things at once:

1. case
2. the attached definite article (the)

In this sentence, both prepositional phrases describe location, not movement, so both nouns are in the dative:

• á svölunum
• í sólskininu

More specifically:

• svölunum = dative plural definite of svalir
• sólskininu = dative singular definite of sólskin

Icelandic usually attaches the to the end of the noun instead of putting a separate word before it.

Because this sentence is about being in a place, not moving to a place.

A very important Icelandic pattern is:

• location -> often dative
• motion toward/into/onto -> often accusative

So here:

• Ég sit á svölunum = I am sitting on the balcony.
  Location -> dative
• Ég fer út á svalirnar = I go out onto the balcony.
  Movement -> accusative

And similarly:

• í sólskininu = in the sunshine
  Location -> dative

This location-vs-motion contrast is one of the most important things to notice with Icelandic prepositions.

Because the noun changes form in the dative plural, and there is also a vowel change.

The base form is:

• svalir

But in the dative plural it becomes:

• svölum

And with the definite article added:

• svölunum

That a -> ö change is a normal kind of Icelandic vowel alternation, not something unique to this word. So yes, this is a form you largely have to learn, but it follows common Icelandic patterns.

Because Icelandic usually expresses the by attaching it to the noun.

So instead of a separate word like English the, Icelandic often uses a noun ending:

• svalir = balconies / balcony

• svölunum = the balcony / the balconies, in the dative plural

• sólskin = sunshine
• sólskininu = the sunshine, in the dative singular

This is why Icelandic words can look long: the noun, case ending, and definite article are often all packed into one form.

Yes. The sentence as given is a very natural neutral order:

• Ég sit á svölunum í sólskininu.

But Icelandic word order is somewhat flexible, especially if you want to emphasize something. For example:

• Í sólskininu sit ég á svölunum.

That puts í sólskininu first for emphasis. Notice that the verb still comes early: Icelandic follows the verb-second pattern in main clauses.

So the original sentence is the most straightforward version, but other orders are possible depending on emphasis.

Yes, there is a small difference in meaning.

• í sólskininu = in the sunshine / in the sunlight
• í sólinni = in the sun

Both can be natural, but sólskin focuses more on the sunshine/light, while sólin means the sun itself.

So this sentence gives a slightly more vivid feeling of sitting there with the sunshine around you.