Koddaverið er þurrt núna, en sængurverið þarf aðeins lengri tíma.

Because Icelandic usually adds the definite article to the end of the noun instead of putting a separate word like the in front.

• koddaver = pillowcase

• koddaverið = the pillowcase

• sængurver = duvet cover
• sængurverið = the duvet cover

Here, -ið is the definite ending for these neuter singular nouns.

Both are neuter nouns. That matters because adjectives and some endings in Icelandic have to agree with the noun’s:

• gender
• number
• case

So because koddaverið is neuter singular, the adjective becomes þurrt and not þurr.

Because þurrt agrees with a neuter singular noun.

The basic adjective is þurr = dry.
When it describes a neuter singular subject, it becomes þurrt.

So:

• Koddaverið er þurrt = The pillowcase is dry.

If the noun were masculine or feminine, the form would be different.

Because here the adjective is being used predicatively, not directly before the noun.

• koddaverið er þurrt = the pillowcase is dry
• þurra koddaverið or similar pre-noun use would be a different structure, more like the dry pillowcase

So in this sentence, þurrt comes after er because it is part of the statement about the subject.

Núna means now / right now.

It is very close in meaning to nú. In everyday speech, núna often feels a little more conversational or a little more immediate.

So:

• nú = now
• núna = now, right now

In this sentence, núna simply tells you the drying state at this moment.

No, nothing is omitted. The second clause has a different verb.

• er = is
• þarf = needs

So the structure is:

• Koddaverið er þurrt núna = The pillowcase is dry now
• en sængurverið þarf aðeins lengri tíma = but the duvet cover needs a little longer time

English also does this naturally: It is dry, but the other one needs more time.

Because its subject is singular: sængurverið.

Even though the whole sentence mentions two different items, each clause has its own subject:

• Koddaverið ... er
• sængurverið ... þarf

Since sængurverið is singular, the verb is singular too.

There are two things happening here:

1. tími changes to tíma
   That is because þurfa normally takes an accusative object.
   So tími becomes tíma.

2. lengri is the comparative form of langur
   Here it means longer.

So:

• tími = time
• lengri tíma = a longer time

In natural English, this is often translated as a bit longer or a little more time.

Because lengri is agreeing with tíma, which is a masculine singular noun here.

A very useful idea is:

• lengri = longer, in many common masculine/feminine contexts
• lengra = often used with neuter singular

So in lengri tíma, the masculine noun tími leads to lengri.

Here aðeins means something like only, just, or a little.

In this sentence, it softens the comparison:

• aðeins lengri tíma = just a little longer, a little more time

So the sense is not that the duvet cover needs a lot more time, only a bit more.

Yes. Icelandic word order is more flexible than English word order.

For example, you could also hear:

• Koddaverið er núna þurrt

That still means basically the same thing. The version in your sentence,

• Koddaverið er þurrt núna

is very natural and straightforward.

They are compound nouns, which are very common in Icelandic.

• koddi = pillow
• ver = cover/case

• koddaver = pillowcase

• sæng = duvet / quilt / bedclothes
• ver = cover
• sængurver = duvet cover

Notice that compounds do not always combine in a perfectly obvious way for English speakers, so it is worth learning them as whole words too.

A good beginner rule is:

• þ is like th in thin
• ð is like th in this

So in this sentence:

• þurrt starts with the thin sound
• aðeins contains the this sound

That said, real Icelandic pronunciation can be a bit more subtle than English, especially in fast speech, but this rule is an excellent starting point.