Röðin er styttri í dag.

Röð is the basic noun, meaning something like line / queue / row / sequence, depending on context.

Röðin is the definite form: the line.
In Icelandic, the definite article is usually added to the end of the noun instead of being a separate word like English the.

So:

• röð = a line / line
• röðin = the line

Here, the sentence is talking about a specific line, so röðin is used.

It is nominative singular.

That is because röðin is the subject of the sentence, and subjects are normally in the nominative case in Icelandic.

You can think of the structure as:

• Röðin = subject
• er = is
• styttri = shorter
• í dag = today

Er is the 3rd person singular present form of vera, which means to be.

Since röðin is singular, the verb is singular too:

• röðin er = the line is

If the subject were plural, you would use eru instead:

• raðirnar eru styttri = the lines are shorter

Styttri is the comparative form of the adjective stuttur, which means short.

So the forms are:

• stuttur = short
• styttri = shorter

This is not formed in a completely transparent way for English speakers, because the stem changes:

• u changes to y
• the comparative ending is added

So you have to learn stuttur → styttri as a pattern.

Because it agrees with röðin, which is feminine singular nominative.

In Icelandic, adjectives often agree with the noun they describe in gender, number, and case. That also applies when the adjective comes after vera and works like a predicate adjective.

Here:

• röðin = feminine singular nominative
• so the adjective appears as styttri

A useful comparison:

• bíllinn er styttri = the car is shorter
• röðin er styttri = the line is shorter
• húsið er styttra = the house is shorter

So the form can change depending on the noun.

No. Röð can mean several related things, depending on context:

• queue / line
• row
• order
• sequence / series

In this sentence, because of styttri í dag, the most natural meaning is usually queue / line.

So if you saw this in a shop, bank, or café, it would most likely mean the line is shorter today.

Literally, í dag means in day, but as a fixed Icelandic expression it means today.

This is a very common time expression. You should learn it as a unit:

• í dag = today
• í gær = yesterday
• á morgun = tomorrow

So even though it looks a bit different from English, it functions just like the English adverb today in this sentence.

The dictionary form is dagur = day.

In the phrase í dag, the noun appears in a different case form, not the dictionary form. Icelandic nouns change form depending on case.

So:

• dagur = nominative
• dag = another case form used here in the expression í dag

For learners, the easiest approach is to memorize í dag as a whole phrase meaning today.

Yes. Icelandic word order is flexible, though not random.

You can also say:

• Í dag er röðin styttri.

That puts more emphasis on today.

Both versions are natural, but the emphasis is slightly different:

• Röðin er styttri í dag. = neutral statement
• Í dag er röðin styttri. = today, the line is shorter

Yes, very much so.

The pattern is:

• something is + comparative adjective + time expression

So:

• Röðin er styttri í dag.
• literally: The line is shorter today.

This works very similarly to English, which makes the sentence structure quite learner-friendly.

You would use the comparative of langur (long):

• Röðin er lengri í dag.

So:

• styttri = shorter
• lengri = longer

This is a good pair to learn together.

Yes, a few:

• ö in röðin does not have an exact English equivalent.
• ð in röðin is like the th in this, not the th in thin.
• y in styttri is pronounced more like Icelandic i than like English y.
• Icelandic r is usually trilled or tapped, not pronounced like a typical English r.

So the spelling may look familiar in places, but the sounds are often different from what an English speaker would first expect.