Söngkonan varð fræg í fyrra.

The ending -an is the attached definite article in Icelandic.

• söngkona = female singer
• söngkonan = the female singer

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

So:

• kona = woman
• konan = the woman

The same pattern is happening here with söngkona → söngkonan.

The basic dictionary form is söngkona.

This is a compound word:

• söng- = song / singing
• kona = woman

So söngkona literally means something like song-woman, i.e. female singer.

In this sentence, it appears as söngkonan, which is the nominative singular definite form: the singer.

Yes. Söngkona specifically means a female singer.

A common word for male singer is:

• söngvari

Depending on context, söngvari can also sometimes be used more generally for singer, but söngkona clearly marks the person as female.

So this sentence is specifically about a female singer.

Because verða is the infinitive, and varð is its past tense form.

• verða = to become
• varð = became

In this sentence, the subject is singular, so Icelandic uses the 3rd person singular past form:

• ég verð = I become
• hún verður = she becomes
• hún varð = she became

So Söngkonan varð... means The singer became...

Because fræg is agreeing with söngkonan, which is feminine singular nominative.

After verbs like verða (to become), Icelandic often uses a predicate adjective that matches the subject in gender, number, and case.

Here:

• söngkonan = feminine singular nominative
• so the adjective is also feminine singular nominative: fræg

Compare:

• maðurinn varð frægur = the man became famous
• konan varð fræg = the woman became famous
• barnið varð frægt = the child became famous

So fræg is exactly the form you expect with a feminine subject.

Because it describes the subject, not a direct object.

In Söngkonan varð fræg, the singer is the one who became famous. The adjective fræg is linked back to the subject through the verb varð.

This is similar to how Icelandic uses nominative after verbs like:

• vera = to be
• verða = to become

So:

• Hún er fræg. = She is famous.
• Hún varð fræg. = She became famous.

In both cases, the adjective agrees with the subject.

Í fyrra means last year.

It is a very common time expression in Icelandic and is best learned as a fixed phrase.

Examples:

• í fyrra = last year
• í sumar = this summer / during the summer
• í vetur = this winter / during the winter

So in your sentence, í fyrra tells you when she became famous.

Because Icelandic expresses this time phrase differently from English.

English says:

• last year

But Icelandic uses the fixed expression:

• í fyrra

Even though í often means in, you should not translate this word-for-word too mechanically here. The whole phrase simply means last year.

This is very common when learning Icelandic: some time expressions use structures that do not match English exactly.

In í fyrra, fyrra is part of an old comparative-based form related to fyrri, meaning earlier / former.

In modern learning terms, the easiest and most useful thing is to treat í fyrra as a set phrase meaning last year.

You do not usually need to analyze it every time you use it. Just learn:

• í fyrra = last year
• á þessu ári = this year
• á næsta ári = next year

A rough learner-friendly pronunciation guide would be:

• Söngkonan ≈ SUNG-koh-nan
• varð ≈ varth or vahrth
• fræg ≈ something like frigh with an eye-like vowel
• í = ee
• fyrra ≈ FIR-ra

A few important pronunciation notes:

• ö does not sound like English o. It is closer to the vowel in French peur or German schön, though exact matches are hard.
• ð is like the th in this, but in some positions in Icelandic it is pronounced more weakly or differently than English speakers expect.
• æ in fræg is pronounced roughly like eye.
• rr in fyrra is strongly pronounced.

If you want to sound natural, it is best to listen to native audio, because Icelandic spelling and pronunciation do not always match English expectations.

Because this is the normal Icelandic sentence structure here:

• Subject + verb + complement + time expression

So:

• Söngkonan = subject
• varð = verb
• fræg = complement/predicate adjective
• í fyrra = time expression

That order is very natural in Icelandic.

You could move the time phrase for emphasis, for example:

• Í fyrra varð söngkonan fræg.

That still means the same thing, but now last year is emphasized more.

Yes. In natural English, became famous and got famous can express nearly the same idea.

In Icelandic, varð fræg literally corresponds to became famous:

• verða = become
• varð = became

So got famous is a possible natural translation in English, even though the Icelandic grammar is built around become rather than get.

Yes, but it means something different.

• Söngkonan varð fræg í fyrra. = The singer became famous last year.
• Söngkonan var fræg í fyrra. = The singer was famous last year.

So:

• varð focuses on the change into being famous
• var simply describes the state of already being famous at that time

That is an important distinction in Icelandic.