Við klárum lokahreingerninguna og lokum ruslagáminum.

They are both present tense, 1st person plural verb forms.

• við klárum = we finish
• við lokum = we close

So the ending -um here is the we form. Icelandic often shows person and number directly on the verb.

Because the same subject applies to both verbs.

The structure is basically:

• Við klárum ... og lokum ...

That works like English We finish ... and close .... You do not have to repeat we before the second verb unless you want extra emphasis or clarity.

Icelandic uses compound words very freely.

lokahreingerning is one compound noun made from:

• loka- = final / end / closing
• hreingerning = cleaning

So instead of writing something like two separate words, Icelandic often combines them into a single noun.

A useful rule: in Icelandic compounds, the last part is usually the main noun, and it determines things like gender.

Because it is:

• singular
• definite
• accusative
• feminine

The dictionary form is lokahreingerning.

In this sentence it is the object of klára, and klára takes the accusative. Icelandic also usually attaches the to the end of the noun instead of using a separate word.

So lokahreingerninguna means something like the final cleaning in the accusative form.

Because it is a different noun with a different gender, and it is in a different case.

The dictionary form is ruslagámur. In this sentence, the verb loka takes a dative object, not an accusative one.

So:

• ruslagámur = nominative singular
• ruslagámi = dative singular
• ruslagáminum = dative singular definite

This is very common in Icelandic: different verbs require different cases for their objects.

A very useful pattern to memorize is:

• klára eitthvað = finish something (accusative)
• loka einhverju = close something (dative)

Because Icelandic usually uses a suffixed definite article.

Instead of a separate word like English the, Icelandic often adds the definite article directly to the noun:

• lokahreingerning → lokahreingerninguna
• ruslagámur → ruslagáminum

Those endings do more than just mean the. They also show things like:

• case
• number
• gender

Yes. Og is the ordinary coordinating conjunction and.

Here it joins two actions with the same subject:

• Við klárum ... og lokum ...

Not exactly.

• In lokum, you have the verb loka in a finite form: we close
• In lokahreingerninguna, loka- is part of a compound noun meaning something like final / end / closing

So they are related in idea, but they are not the same grammatical thing in this sentence.

A good vocabulary list would be:

• við = we
• klára = to finish
• lokahreingerning = final cleaning / final cleanup
• loka = to close
• ruslagámur = dumpster / trash container

It is also worth learning the verbs together with the case they require:

• klára + accusative
• loka + dative

A few useful things:

• Icelandic stress is usually on the first syllable
• á is a separate letter, not just a marked a
• á is roughly like the vowel in English cow
• ð in við is a soft sound, like the th in this, though at the end of a word it can sound weaker

So when reading the sentence, pay special attention to:

• klárum
• gá in ruslagáminum
• við

The accents matter in Icelandic spelling and pronunciation; they are not optional.