Hún spilar bæði á fiðlu og hljómborð, sem mér finnst mjög skemmtilegt.

Bæði ... og ... means both ... and ....

So:

• bæði á fiðlu og hljómborð = both violin and keyboard

It is a very common Icelandic pairing, just like English both ... and .... It can connect nouns, phrases, or even larger parts of a sentence.

With musical instruments, Icelandic normally uses spila á + instrument.

So you say:

• spila á fiðlu = play the violin
• spila á píanó = play the piano
• spila á gítar = play the guitar

This is just the standard Icelandic construction. English does not use a preposition here, but Icelandic usually does.

Because the same preposition applies to both nouns.

So á in:

• á fiðlu og hljómborð

covers both fiðlu and hljómborð.

This is very normal in Icelandic. Repeating the preposition would usually be unnecessary:

• á fiðlu og hljómborð = natural
• á fiðlu og á hljómborð = possible, but heavier and less streamlined

After spila á in the meaning play an instrument, the noun is normally in the accusative.

That gives:

• fiðla → fiðlu in the accusative singular
• hljómborð → hljómborð in the accusative singular

A useful thing to notice is that hljómborð has the same form in the nominative and accusative singular, so it does not visibly change here.

Also, fiðlu can look confusing because that form is not only accusative, but also dative and genitive singular. In this sentence, though, the important point is that it is the correct form after spila á.

Icelandic usually uses a bare noun in this kind of expression when talking about playing an instrument in general.

So:

• spila á fiðlu
• spila á hljómborð

are normal.

This is different from English, which often says play the violin. Icelandic does not need a definite article here.

Here sem refers to the whole previous idea, not just the last noun.

So the meaning is roughly:

• She plays both violin and keyboard, which I find very fun/interesting.

In other words, the speaker thinks the whole fact that she plays both instruments is interesting or enjoyable.

It is not most naturally understood as:

• keyboard, which I find very fun

No. Sem is very convenient because it does not change form.

Unlike some relative words in other languages, Icelandic sem stays the same whether it refers to:

• a masculine noun
• a feminine noun
• a neuter noun
• a plural noun
• or even an entire clause or idea

That is one reason it is so common.

Because the verb here is finnast, and with finnast the person who has the opinion or impression is put in the dative.

So:

• mér = to me
• mér finnst = I think / I find / it seems to me

You do not say ég finnst.

A helpful way to remember it is that mér finnst is often closer in structure to it seems to me than to a straightforward English I think.

Not exactly.

These are related, but they are used differently:

• finna often means find, feel, or discover
• finnast often means seem or be found/considered

In this sentence, mér finnst mjög skemmtilegt means something like:

• I find it very fun
• it seems very enjoyable to me

So this is the finnast pattern, not ordinary finna.

Because skemmtilegt is describing an idea or whole situation, not a specific feminine or masculine noun.

When Icelandic comments on an entire statement, it very often uses a neuter singular adjective:

• það er skemmtilegt
• mér finnst það skemmtilegt

In this sentence, the clause introduced by sem refers to the whole fact that she plays both instruments, so the adjective appears in the neuter singular:

• skemmtilegt

If it were describing a feminine noun directly, you would expect a feminine form instead.

Here hljómborð means a musical keyboard or keyboard instrument, not a computer keyboard.

Because the verb is spilar and the context is musical instruments, the meaning is clearly musical. Depending on context, it could suggest something like a keyboard, electric keyboard, or synthesizer-type instrument.

The comma helps show that sem mér finnst mjög skemmtilegt is an added comment on the whole previous statement.

So the structure is:

• main statement: Hún spilar bæði á fiðlu og hljómborð
• added comment: sem mér finnst mjög skemmtilegt

This works a lot like an English non-restrictive which-clause:

• ..., which I find very fun.

The comma makes that relationship clearer.