Á skýlausum kvöldum sjáum við oft fleiri stjörnur í sveitinni en í borginni.

This is because Icelandic follows the V2 rule in main clauses: the finite verb usually comes in the second position.

Here, Á skýlausum kvöldum is placed first for emphasis, so the verb must come next:

• Á skýlausum kvöldum = first element
• sjáum = second element
• við = subject

So Á skýlausum kvöldum sjáum við... is completely natural. If you started with Við, then you would say Við sjáum... instead.

Because the preposition á often takes the dative when it is used in time expressions like on / during.

So:

• á kvöldum = in the evenings / on evenings
• á skýlausum kvöldum = on cloudless evenings

Since kvöldum is dative plural, the adjective has to match it:

• skýlausum = dative plural
• kvöldum = dative plural

Skýlaus means cloudless.

It is built from:

• ský = cloud
• laus = without, free from

This is a very common Icelandic pattern. So skýlaus literally means something like without clouds.

In the sentence, it appears as skýlausum because it must agree with kvöldum in case and number.

Sjáum is the 1st person plural present tense of sjá (to see).

So:

• ég sé = I see
• við sjáum = we see

In the sentence, sjáum við means we see.

That is the most natural placement here.

Because of the V2 rule, once the verb sjáum has come second, the subject við follows it, and then adverbs like oft often come after the subject:

• Á skýlausum kvöldum sjáum við oft...

This is a very normal Icelandic word order. You may see other placements in other contexts, but this one is neutral and natural.

Because stjörnur (stars) are countable.

In Icelandic:

• fleiri = more with countable things
• meiri = more with uncountable things, quantity, or abstract ideas

So:

• fleiri stjörnur = more stars
• meira vatn = more water

That is why fleiri is the correct word here.

Because it is the direct object of sjáum.

The verb sjá normally takes an object in the accusative, so:

• stjörnur here is the accusative plural of stjarna

The phrase fleiri stjörnur means more stars, and the noun stays in the plural because we are talking about multiple stars.

Because the sentence is talking about stars in general, not a specific known set of stars.

• stjörnur = stars
• stjörnurnar = the stars

Here the idea is simply that you can see more stars in one place than another, so the indefinite form is the natural choice.

Because í takes the dative when it describes location rather than movement.

Here the meaning is:

• in the countryside
• in the city

So these are locations, not motion toward them.

Compare:

• í sveitinni = in the countryside (location, dative)
• í sveitina = into the countryside (movement, accusative)

The same rule applies to í borginni.

It is part of the definite form: the countryside and the city.

Both sveit and borg are feminine nouns, and here they are in the dative singular definite form:

• sveitinni = in the countryside
• borginni = in the city

So the ending shows both:

• definiteness (the)
• dative singular

Here en means than.

It is used after a comparative expression:

• fleiri ... en ... = more ... than ...

So:

• fleiri stjörnur í sveitinni en í borginni
• more stars in the countryside than in the city

This is the normal way to make this kind of comparison in Icelandic.

Yes, absolutely.

That version is also correct and natural. The difference is mainly one of focus:

• Við sjáum oft... = more neutral, starting with the subject
• Á skýlausum kvöldum sjáum við... = puts special focus on when this happens

So the original sentence foregrounds the time expression: on cloudless evenings.