Installatøren sjekker luft-til-luft-varmepumpen.

Because both nouns are in the definite singular form in Bokmål.

• installatør = installer

• installatøren = the installer

• varmepumpe = heat pump
• varmepumpen = the heat pump

For many common-gender nouns in Norwegian, you make the definite singular by adding -en.

So instead of using a separate word like English the, Norwegian often attaches the definiteness to the end of the noun.

In Norwegian, the definite article is usually attached to the noun as a suffix.

So:

• the installer → installatøren
• the heat pump → varmepumpen

This is one of the big differences from English. English uses a separate word (the), but Norwegian usually adds the definite ending directly to the noun.

A separate determiner can appear in some other structures, especially with adjectives, for example:

• den nye varmepumpen = the new heat pump

But in your sentence, there are no adjectives, so the suffix alone is enough.

Sjekker is the present tense of å sjekke.

• å sjekke = to check
• sjekker = checks / is checking

In a simple sentence like this, Norwegian present tense can correspond to either English checks or is checking, depending on context.

Examples:

• Installatøren sjekker varmepumpen.
  = The installer checks the heat pump / The installer is checking the heat pump

Norwegian verbs are also much simpler than English verbs in many ways, because they do not change for person:

• jeg sjekker = I check
• du sjekker = you check
• han/hun sjekker = he/she checks

Same verb form throughout.

Yes. Å sjekke is a loanword based on English check.

That means it is often easy for English speakers to recognize and remember.

However, Norwegian also has other verbs that can overlap in meaning, depending on context, such as:

• å kontrollere = to inspect / to check / to control
• å undersøke = to examine / investigate

In everyday language, å sjekke is very common and natural.

Because Norwegian often builds long compound nouns, and this one includes a fixed technical expression.

Here the main noun is:

• varmepumpe = heat pump

And it is being specified as a:

• luft-til-luft-varmepumpe = air-to-air heat pump

The luft-til-luft part is hyphenated because it is a compound modifier meaning air-to-air. Then it is attached to varmepumpe, giving a larger compound.

So the whole thing functions as one noun phrase:

• luft-til-luft-varmepumpen = the air-to-air heat pump

This kind of long compound is very normal in Norwegian.

Literally, it means air-to-air.

• luft = air
• til = to
• luft = air

It describes the type of heat pump: one that transfers heat from air to air, rather than, for example, from air to water.

So this is technical vocabulary, and the structure is quite close to English.

The sentence uses the normal Norwegian main-clause order:

Subject + Verb + Object

• Installatøren = subject
• sjekker = verb
• luft-til-luft-varmepumpen = object

So:

• Installatøren sjekker luft-til-luft-varmepumpen.

This is very similar to standard English word order:

• The installer checks the air-to-air heat pump.

Norwegian does have special word-order rules, especially the verb-second rule, but in a simple statement like this, it looks very straightforward.

Normally, no. That would sound incomplete or unnatural here.

If you mean the installer, you need:

• installatøren

If you mean an installer, you would usually say:

• en installatør

So the likely options are:

• Installatøren sjekker luft-til-luft-varmepumpen.
  = The installer checks the air-to-air heat pump.

• En installatør sjekker luft-til-luft-varmepumpen.
  = An installer is checking the air-to-air heat pump.

Bare installatør without any article or ending is generally not right in this sentence.

The beginning sj is pronounced roughly like English sh.

So sjekker sounds approximately like:

• SHEK-er

A few helpful notes:

• sj usually gives a sh-like sound
• the e in sjekk- is short
• the double kk helps show that the preceding vowel is short

So an English speaker can often get quite close by thinking of checker without the English final r sound being too strong, depending on accent.

Because the whole expression is one compound noun, and in Norwegian the definite ending is added to the main noun, which comes at the end.

Structure:

• luft-til-luft- = modifier
• varmepumpe = main noun

Then the definite suffix is added to the main noun:

• varmepumpe → varmepumpen

So:

• luft-til-luft-varmepumpe = air-to-air heat pump
• luft-til-luft-varmepumpen = the air-to-air heat pump

This is very typical in Norwegian compounds: the grammatical ending goes on the final element.