Ég þvæ gaffalinn eftir kvöldmat.

Because þvo is the infinitive, meaning to wash. In the sentence, the verb is conjugated for 1st person singular present tense: ég þvæ = I wash.

This verb is a bit irregular, so the vowel changes:

• að þvo = to wash
• ég þvæ = I wash
• þú þværð = you wash
• hann/hún/það þvær = he/she/it washes

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word.

So:

• gaffall = fork
• gaffalinn / gaffallinn = the fork, depending on case

This is very normal in Icelandic. English uses a separate word the, but Icelandic usually uses a suffix such as -inn, -in, or -ið.

Because the noun is the direct object of þvæ, so it appears in the accusative case.

For this noun:

• nominative singular definite: gaffallinn
• accusative singular definite: gaffalinn

So the sentence uses gaffalinn because I wash takes a direct object in the accusative.

That happens because the noun changes form when it goes from nominative to accusative.

The basic pattern is:

• gaffall = nominative singular
• gaffal = accusative singular

Then the definite ending is added:

• gaffallinn = the fork, as subject
• gaffalinn = the fork, as object

So the missing l is not random; it is part of the noun’s case pattern.

Because kvöldmatur changes form outside the nominative. After the preposition eftir, the noun is in the dative, and the dative singular form is kvöldmat.

So:

• kvöldmatur = dinner/evening meal, nominative
• kvöldmat = dinner/evening meal, dative

This kind of -ur dropping is very common in masculine nouns.

Here eftir means after, and in that meaning it normally takes the dative.

So eftir kvöldmat means after dinner, with kvöldmat in the dative. A useful thing to remember is that some Icelandic prepositions always require a certain case, so you often have to learn the preposition and its case together.

Because this is a general expression, much like English after dinner. Icelandic often leaves out the article with meals in this kind of phrase.

So:

• eftir kvöldmat = after dinner
• eftir kvöldmatinn would mean something more like after the dinner, referring to a specific dinner

Both are possible, but the version without the article is very natural for a general routine statement.

Yes. You can say:

Eftir kvöldmat þvæ ég gaffalinn.

That is still correct. But Icelandic has a verb-second pattern, so if you move eftir kvöldmat to the front, the finite verb þvæ must come next, before ég.

So:

• Ég þvæ gaffalinn eftir kvöldmat.
• Eftir kvöldmat þvæ ég gaffalinn.

Both are good, just with different emphasis.

A rough English approximation is thvai.

Two important parts:

• þ is like the th in thin
• æ is pronounced roughly like ai in eye

So þvæ sounds approximately like thvai, though the real Icelandic pronunciation is a bit tighter and more precise than the English approximation.

By itself, the Icelandic present tense can cover several meanings that English separates.

So Ég þvæ gaffalinn eftir kvöldmat could mean:

• I wash the fork after dinner
• I’m washing the fork after dinner, depending on context
• a habitual action, if that fits the situation

Icelandic does not rely on a separate progressive form as much as English does. Context usually tells you whether it is a general habit or something happening now.

Normally, yes, you should include ég. Icelandic usually keeps subject pronouns, unlike some languages where they are often omitted.

So the normal full sentence is:

• Ég þvæ gaffalinn eftir kvöldmat.

Leaving out ég would usually sound incomplete unless the context is very special, such as a note, a heading, or very informal speech.