Hver gang brandalarmen lyder, følger vi flugtvejsskiltet.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

In this sentence, Hver gang brandalarmen lyder is placed first as an introductory clause. That takes up the first slot, so the main clause must begin with the finite verb:

• Hver gang brandalarmen lyder, følger vi flugtvejsskiltet.

If the sentence started directly with the subject, then you would get:

• Vi følger flugtvejsskiltet, hver gang brandalarmen lyder.

So følger vi is not random word order; it is a very common Danish pattern.

Hver gang means every time or whenever. It emphasizes that the action happens repeatedly, on each occasion.

So:

• hver gang = every time / each time
• når = often when, and sometimes also whenever depending on context

In many situations, når would also be possible:

• Når brandalarmen lyder, følger vi flugtvejsskiltet.

That still sounds natural. But hver gang is a little more explicit about repetition.

Because Hver gang brandalarmen lyder is a subordinate clause, and it is followed by the main clause.

Danish normally separates a subordinate clause from the main clause with a comma:

• Hver gang brandalarmen lyder, følger vi flugtvejsskiltet.

So the comma marks the boundary between:

• the time clause: Hver gang brandalarmen lyder
• the main clause: følger vi flugtvejsskiltet

Because Danish forms compound nouns by writing them as one word.

Here:

• brand = fire
• alarm = alarm
• brandalarm = fire alarm

Then Danish adds the definite article to the end of the noun:

• brandalarm = a fire alarm
• brandalarmen = the fire alarm

So brandalarmen is made of:

• brand + alarm + en

Writing it as separate words would be wrong in standard Danish.

For the same reason: Danish loves compound nouns.

This word is built from smaller parts:

• flugtvej = escape route / evacuation route
• skilt = sign
• flugtvejsskilt = escape-route sign
• flugtvejsskiltet = the escape-route sign

The -s- in the middle is a linking sound often found in Danish compounds:

• flugtvej + skilt → flugtvejsskilt

Then the definite ending -et is added:

• flugtvejsskiltet = the escape-route sign

Because Danish nouns have two grammatical genders:

• common gender
• neuter gender

In the singular definite form, they usually take different endings:

• common gender: -en
• neuter gender: -et

So here:

• en brandalarm → brandalarmen
• et skilt → skiltet

That is why you get:

• brandalarmen
• flugtvejsskiltet

This is something you usually have to learn together with the noun: en noun or et noun.

Lyder is the present tense of at lyde.

• at lyde = to sound / to ring
• lyder = sounds / rings

Danish present tense is often formed with -r, so this is a very normal verb form.

In this sentence, the present tense is used for a general rule or repeated situation, not just something happening right now. English does something similar:

• When the alarm sounds, we follow the sign.

So the present tense here expresses a routine or instruction.

For the same reason: the sentence describes a general procedure.

• følger = present tense of at følge = to follow

The sentence is not telling a story about one specific past event. It describes what people do as a rule in that situation. Danish commonly uses the present tense for:

• routines
• instructions
• general truths
• rules

So both verbs are in the present because the whole sentence describes a standing instruction.

Because at følge normally takes a direct object.

Here the thing being followed is:

• flugtvejsskiltet

So the structure is simply:

• følge noget/nogen = follow something/someone

That is similar to English:

• follow the sign
• follow the route
• follow the teacher

No extra preposition is needed.

No. At følge is quite flexible in Danish.

It can mean:

• physically follow: følge skiltet
• follow instructions/rules: følge reglerne
• follow a story/conversation: følge med i filmen

In this sentence, it most naturally means something like follow the direction indicated by the escape-route sign. So it is connected to movement, safety procedure, and guidance.

Yes. Danish allows that too:

• Vi følger flugtvejsskiltet, hver gang brandalarmen lyder.

That version is also correct.

The difference is mostly about focus:

• Hver gang brandalarmen lyder, følger vi flugtvejsskiltet.
  Focuses first on the situation/time.
• Vi følger flugtvejsskiltet, hver gang brandalarmen lyder.
  Focuses first on what we do.

Both are natural; the original just gives prominence to the time condition first.