Frostið á rúðunni bráðnar þegar sólin skín.

Frost is the basic noun, and -ið is the definite article attached to the end. So frostið means the frost.

In this sentence, frostið is also the subject of the main clause, so it is in the nominative singular. Because frost is a neuter noun, the definite form here is frostið.

Here á means on, and it is being used for location: the frost is on the window.

With many Icelandic prepositions, the case changes depending on meaning. Á often takes:

• dative for location: on
• accusative for motion toward something: onto

Since the frost is already sitting on the window, Icelandic uses the dative, so:

• rúða = window / pane
• rúðunni = the window / the pane in dative singular

More literally, rúða means pane, windowpane, or the glass part of a window.

But in everyday Icelandic, especially in contexts like frost, rain, or condensation, rúða is often used where English would naturally say window. So á rúðunni is very naturally understood as on the window.

Because the frost is on the surface of the glass, not inside something.

• á = on
• í = in / inside

So á rúðunni is the natural choice for frost on a windowpane.

For the same reason as frostið: Icelandic usually adds the as an ending.

• sól = sun
• sólin = the sun

Here sólin is the subject of skín, so it is in the nominative singular. Sól is a feminine noun, and the definite nominative singular form is sólin.

Þegar means when and introduces a subordinate clause:

• þegar sólin skín = when the sun shines

It connects the two parts of the sentence:

• main clause: Frostið á rúðunni bráðnar
• subordinate clause: þegar sólin skín

Both are present tense, 3rd person singular:

• bráðnar = melts
• skín = shines

This is a very common way to express a general truth or regular situation, just as in English:

• The frost melts when the sun shines.

No. This is an important difference.

• bráðna = to melt intransitive, meaning something melts by itself
• bræða = to melt something transitive

So:

• Frostið bráðnar = The frost melts
• Sólin bræðir frostið = The sun melts the frost

In your sentence, bráðnar is used because the frost is the thing undergoing the change.

The subject is the whole noun phrase Frostið á rúðunni.

The head noun is frostið, and á rúðunni modifies it by telling you which frost: the frost on the window.

So the verb bráðnar agrees with frostið, not with rúðunni.

Because Icelandic usually expresses definiteness by attaching the article to the noun itself.

In this sentence:

• frostið = the frost
• rúðunni = the window in dative
• sólin = the sun

So English uses a separate word the, but Icelandic often builds that meaning into the noun ending.

Yes. Icelandic is a verb-second language in main clauses.

So if the sentence begins with the þegar-clause, the finite verb of the main clause usually comes next:

• Þegar sólin skín, bráðnar frostið á rúðunni.

That is the normal Icelandic order.

An English speaker may want to say something like Þegar sólin skín, frostið á rúðunni bráðnar, but standard Icelandic prefers the verb-second pattern: bráðnar comes right after the opening clause.