Læknirinn mælti með smá fríi frá vinnu um helgina.

Because Icelandic usually adds the definite article directly to the noun instead of using a separate word like the.

• læknir = doctor
• læknirinn = the doctor

So -inn here is the masculine singular definite ending in the nominative.

It means recommended or advised in favor of. This is a fixed expression you should learn as a unit:

• mæla can mean things like measure, say/speak, or in some contexts recommend
• mæla með + dative = recommend

So the með is not optional here; it is part of the expression.

Mælti is the past tense, 3rd person singular form of mæla.

It matches the subject læknirinn because that subject is singular. Icelandic verbs do not change for gender here, only for person and number.

Because með takes the dative case in this meaning, so the noun after it has to be in dative.

The noun frí has these main singular forms:

• nominative/accusative: frí
• dative: fríi

So after með, you get fríi.

In modern Icelandic, smá is very often used as an indeclinable word, especially in everyday language, meaning a little or small.

So even though fríi is dative, smá does not change here:

• smá frí
• smá fríi
• smá vinna

You may also meet the fully declined adjective smár, but smá is extremely common in speech and informal writing.

Because Icelandic does not have an indefinite article like English a/an.

A noun without the definite article is usually just indefinite by itself. So smá fríi naturally means something like:

• a little break
• some time off

If Icelandic wants the, it normally adds it to the noun, as in læknirinn.

Because Icelandic commonly says frí frá vinnu, literally time off from work.

Also, frá takes the dative case. The noun vinna happens to be vinnu in the dative singular, so the form you see is:

• frá vinnu = from work / off work

So even though the ending may look familiar, it is still functioning as dative here.

Um helgina means over the weekend or during the weekend.

In time expressions like this, um takes the accusative, so:

• helgi = weekend
• helgina = the weekend (accusative singular definite)

This phrase is very common when talking about what happens during a particular weekend.

Because Icelandic often uses the definite form in time expressions when the weekend is understood from context, much like English the weekend or this weekend.

So:

• um helgina = over the weekend
• um helgar = on weekends, in general

The definite form makes it sound like a specific relevant weekend, not weekends in general.

Yes, somewhat. The sentence as given has a very natural neutral order:

• Læknirinn mælti með smá fríi frá vinnu um helgina.

But Icelandic word order is flexible, especially with time phrases. For example, you could move um helgina to the front for emphasis:

• Um helgina mælti læknirinn með smá fríi frá vinnu.

Notice that the finite verb mælti still stays in the second position. That is a very important Icelandic pattern.