Røgalarmanlægget og varslingsanlægget virker i hele bygningen.

Danish very often builds compound nouns by joining smaller words into one word.

• røgalarmanlægget = røg
  • alarm
    • anlægget
• varslingsanlægget = varsling(s)
  • anlægget

The last part is the “main” noun, and the earlier parts describe it. So both words are kinds of anlæg, meaning a system, installation, or setup.

That ending is the definite article attached to the noun, like English the.

• et anlæg = a system / an installation
• anlægget = the system / the installation

Because both compounds end in anlæg, and anlæg is a neuter noun (et-word), the definite singular form is -et.

In Danish compounds, an extra -s- is sometimes inserted between the parts. This is often called a linking s.

So:

• varsling
  • anlæg becomes varslingsanlæg
• but røgalarm
  • anlæg stays røgalarmanlæg

There is not always a simple rule you can predict perfectly, so this is something learners often pick up through exposure.

Here virker means works, functions, or is operating.

So it means that the smoke alarm system and the warning system are functioning throughout the building. In other contexts, virke can also mean seem, but not in this sentence.

Because Danish verbs do not change for singular and plural in the present tense.

So:

• systemet virker = the system works
• systemerne virker = the systems work

The verb stays virker either way. That is different from English, where works and work are different.

This means in the whole building or more naturally throughout the building.

• i bygningen = in the building
• i hele bygningen = in the entire building / throughout the building

The word hele adds the idea of total coverage, not just location inside the building.

The adjective hel changes form.

• hel for a common-gender singular indefinite noun
• helt for a neuter singular indefinite noun
• hele for plural or definite nouns

Because bygningen is definite (the building), Danish uses hele:

• hele bygningen = the whole building

So helt bygningen would be wrong here.

Because bygning is a common-gender noun, not a neuter noun.

• en bygning = a building
• bygningen = the building

In Danish, common-gender nouns usually take -en in the definite singular, while neuter nouns usually take -et.

Yes. This is the normal pattern:

Subject + verb + prepositional phrase

• Røgalarmanlægget og varslingsanlægget = subject
• virker = verb
• i hele bygningen = prepositional phrase

A very important Danish rule is that the finite verb is usually in second position in main clauses. If you moved i hele bygningen to the front, the verb would still stay second:

I hele bygningen virker røgalarmanlægget og varslingsanlægget.

Not necessarily in a strict mathematical sense. It usually means throughout the building or across the building as a whole.

In many contexts, that strongly suggests full coverage, but the exact practical meaning depends on the situation. If someone wanted to stress everywhere, they might also say overalt i bygningen.