Tøyet tørker på tørkestativet.

Because both nouns are in the definite singular form.

In Norwegian, the definite article is usually added to the end of the noun instead of being a separate word like English the.

• tøy → tøyet = the laundry / the clothes
• tørkestativ → tørkestativet = the drying rack

The ending -et is typical for many neuter nouns.

Grammatically, tøyet is singular definite, but its meaning is often collective.

That means it can refer to:

• the laundry as a mass of clothing, or
• the clothes as a group

So even though English often uses a plural idea, Norwegian can use singular grammar here.

Both can refer to clothes, but the feeling is a bit different.

• tøyet often means the laundry / the clothes as a batch
• klærne means the clothes / the garments

So:

• Tøyet tørker på tørkestativet. = the laundry is drying on the drying rack
• Klærne tørker på tørkestativet. = the clothes are drying on the drying rack

In this context, tøyet sounds very natural if you are talking about washed clothes drying.

Because Norwegian often uses the simple present where English uses the present progressive.

So tørker can mean:

• dries
• is drying

In everyday Norwegian, Tøyet tørker is the normal way to say The laundry is drying.

If you want to emphasize the ongoing process, you can say something like:

• Tøyet holder på å tørke.

But that is more explicit and not necessary in a normal sentence like this.

Here på means on.

You use på because the clothes are understood as being on the drying rack, hanging or lying on it.

• på tørkestativet = on the drying rack

Using i would mean in, which does not fit a normal drying rack.

It is a compound noun, which is very common in Norwegian.

It is built from:

• tørke = dry
• stativ = stand / rack

So tørkestativ literally means something like drying-stand, which we would normally translate as drying rack.

Then the definite ending is added:

• tørkestativ → tørkestativet

Here it is used intransitively.

That means the laundry is doing the action itself:

• Tøyet tørker. = The laundry is drying.

But tørke can also be used transitively, where someone dries something:

• Jeg tørker tøyet. = I dry the laundry.

So the same verb can work in both ways, depending on the sentence.

The hardest sounds for English speakers are usually ø and y.

A rough guide:

• tøyet: the first part tøy has a diphthong with ø plus y; there is no perfect English equivalent
• tørker: the ø is a rounded vowel, somewhat like the vowel in British bird, but with rounded lips
• tørkestativet: same tørke- beginning as in tørker

A very rough approximation might be:

• TØY-eh TUR-ker po TUR-keh-sta-TEE-veh

But that is only approximate. The vowels are important, especially ø and y.

Yes, but the basic sentence is the most neutral one:

• Tøyet tørker på tørkestativet.

You can move the location first for emphasis:

• På tørkestativet tørker tøyet.

That is still grammatical, but now the sentence emphasizes where the laundry is drying.

Notice that in Norwegian main clauses, the finite verb still stays in second position:

• På tørkestativet
  • tørker
    • tøyet

Yes, but it means something slightly different.

• Tøyet tørker på tørkestativet. = the laundry is drying on the drying rack
• Tøyet er på tørkestativet. = the laundry is on the drying rack

The first sentence focuses on the process of drying.
The second focuses only on the location.