Ég nota tvær þvottaklemmur þegar peysan hangir á þvottasnúrunni úti.

Because þvottaklemmur is a feminine plural noun, and Icelandic two changes form for gender and case.

Here, þvottaklemmur is the direct object of nota, so it is in the accusative plural. The feminine accusative plural form of tveir is tvær.

Compare:

• tveir for masculine
• tvær for feminine
• tvö for neuter

So tvær þvottaklemmur = two clothes pegs / two clothespins.

The form þvottaklemmur is the correct plural form of þvottaklemma.

The noun is feminine, and in this sentence it is:

• plural, because there are two of them
• accusative, because it is the object of nota

For this noun, the nominative plural and accusative plural happen to look the same: þvottaklemmur.

So even though it is the object, the form stays þvottaklemmur.

Because peysan means the sweater, while peysa means just a sweater / sweater.

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

So:

• peysa = sweater
• peysan = the sweater

In this sentence, the speaker is talking about a specific sweater, so peysan is natural.

It is the present tense, third-person singular form of hanga = to hang.

So peysan hangir can mean:

• the sweater hangs
• the sweater is hanging

Icelandic often uses the simple present where English might prefer a continuous form. So you do not need a separate form for is hanging here.

Because á takes different cases depending on whether you mean location or motion.

• á + dative = on something, in a fixed location
• á + accusative = onto something, movement toward it

Here the sweater is already hanging on the clothesline, so this is location, not movement. That is why Icelandic uses the dative:

• á þvottasnúrunni = on the clothesline

If you were talking about putting it onto the line, you would expect the accusative instead.

That ending shows two things at once:

• dative singular
• definite: the

The base noun is þvottasnúra = clothesline.

So:

• þvottasnúra = a clothesline
• þvottasnúrunni = on the clothesline / to the clothesline depending on context, but here specifically on the clothesline

The ending may look complicated, but it is just the noun carrying both case and the definite article.

Úti means outside or outdoors.

So á þvottasnúrunni úti means something like:

• on the clothesline outside
• on the outdoor clothesline

It comes at the end because that is a very natural place for adverbs of location in Icelandic. It adds the detail that this is happening outdoors, not inside.

Both are very typical Icelandic compounds.

• þvottaklemma = laundry/washing clip → clothes peg / clothespin
• þvottasnúra = laundry/washing line → clothesline

The first part, þvotta-, is a linking form related to þvottur (washing, laundry). Icelandic makes compounds very freely, so learning to spot the parts is very helpful.

A rough breakdown is:

• þvotta- = laundry / washing
• klemma = clip
• snúra = cord / line

Because Icelandic usually puts the at the end of the noun as a suffix.

In this sentence:

• peysan = the sweater
• þvottasnúrunni = the clothesline in the dative singular

English uses a separate word, but Icelandic often builds definiteness directly into the noun.

That is one reason Icelandic nouns carry so much information in a single word.

A learner will often want to check all the noun forms. In this sentence:

• Ég — nominative, because it is the subject
• tvær þvottaklemmur — accusative plural, because it is the direct object of nota
• peysan — nominative singular, because it is the subject of hangir
• á þvottasnúrunni — dative singular after á for location

So the sentence is a good example of Icelandic case marking in action.

Because þegar introduces a subordinate clause, and subordinate clauses do not follow the usual main-clause verb-second pattern in the same way.

So you get:

• þegar peysan hangir ... = when the sweater is hanging ...

with the order subject + verb inside that clause.

If you put the þegar clause first in the whole sentence, the main clause would then show inversion:

• Þegar peysan hangir á þvottasnúrunni úti, nota ég tvær þvottaklemmur.

Notice nota ég there.

Yes, some variation is possible.

For example, you could also say:

• Þegar peysan hangir á þvottasnúrunni úti, nota ég tvær þvottaklemmur.

That puts more emphasis on the when-clause first.

You may also hear slightly different placement of úti, such as:

• ... hangir úti á þvottasnúrunni

That still means essentially the same thing. The original sentence is perfectly natural; these are just alternative ways to arrange the information.

Usually, yes, but like English when, it can cover slightly different shades of meaning depending on context.

It can mean:

• when
• sometimes something close to whenever
• in some contexts something like once or as soon as

In this sentence, the most natural reading is simply when:
I use two clothes pegs when the sweater is hanging on the clothesline outside.