Wir halten laut Nutzungsordnung den Fluchtweg frei.

Here laut means according to or as stated in.

So laut Nutzungsordnung means according to the usage rules / regulations.

This is a very common formal or semi-formal word in German, especially in notices, rules, reports, and official language.

Example:

• Laut Vertrag = according to the contract
• Laut Polizei = according to the police

Because Fluchtweg is the direct object of the verb phrase frei halten, so it is in the accusative case.

• nominative: der Fluchtweg
• accusative: den Fluchtweg

The subject is wir, and we are doing something to the escape route, so Fluchtweg becomes the object:

• Wir halten den Fluchtweg frei.

Fluchtweg literally means escape route.

It is often used for:

• emergency exits
• evacuation routes
• areas that must stay clear so people can leave safely in an emergency

In buildings, signs like this often mean Do not block this path.

Because frei is working as a predicate adjective/complement with halten.

The pattern is:

etwas frei halten = to keep something clear / free

So:

• den Fluchtweg frei halten = to keep the escape route clear

German often puts this kind of adjective after the object:

• Die Tür offen halten = to keep the door open
• den Weg frei halten = to keep the way clear
• das Fenster sauber halten = to keep the window clean

So frei is not describing Fluchtweg like an adjective before a noun. It is describing the resulting state of the object.

Not really. Although halten often does mean to hold, in this sentence it means to keep in a certain state.

So:

• frei halten = keep clear
• offen halten = keep open
• sauber halten = keep clean

This is a very common German structure.

Nutzungsordnung is a compound noun:

• Nutzung = use, usage
• Ordnung = order, rules, regulations

Together, Nutzungsordnung means something like:

• usage regulations
• rules for use
• house rules
• terms of use

The best translation depends on context. In a building or shared space, it often means the official rules for using that place.

Laut is a preposition that is often used with the genitive, especially in more formal German.

However, in modern German you may also see it with:

• no article, as here: laut Nutzungsordnung
• sometimes forms that look like dative in everyday usage

In this sentence, because Nutzungsordnung has no article, you do not really see a clear case ending. So it is best just to learn laut + noun as a common fixed pattern meaning according to.

Examples:

• laut Gesetz = according to the law
• laut Bericht = according to the report
• laut den Regeln is also heard, but that is a different structure and less elegant in formal style

Yes. German word order is flexible, especially with adverbial phrases like laut Nutzungsordnung.

You could also say:

Laut Nutzungsordnung halten wir den Fluchtweg frei.

That version sounds very natural too, and it puts more emphasis on according to the regulations.

The finite verb halten still stays in the second position in a main clause:

• Wir | halten | laut Nutzungsordnung den Fluchtweg frei.
• Laut Nutzungsordnung | halten | wir den Fluchtweg frei.

It sounds somewhat formal and a bit like a notice, rule, or statement of compliance.

That is mainly because of:

• laut
• Nutzungsordnung
• the topic of Fluchtweg

In everyday speech, someone might say something simpler, such as:

• Wir halten den Fluchtweg frei.
• Der Fluchtweg muss frei bleiben.

But the original sentence is perfectly natural in a formal or institutional context.

Yes. You will often see freihalten written as one verb.

So these are closely related:

• den Fluchtweg frei halten
• den Fluchtweg freihalten

In practice, freihalten is very common, especially in signs and instructions:

• Fluchtweg freihalten! = Keep escape route clear!

Your sentence uses the same basic idea, just in a full clause:

• Wir halten ... den Fluchtweg frei.

German often leaves out the article after laut, especially in formal language.

So laut Nutzungsordnung is very natural and concise.

You may compare:

• laut Vertrag
• laut Gesetz
• laut Satzung
• laut Nutzungsordnung

This gives the sentence a formal, rule-based tone.