Die Nutzungsordnung gehört zum Nutzungsvertrag.

Because Ordnung is a feminine noun in German, so its nominative singular article is die.

Here, die Nutzungsordnung is the subject of the sentence, so it stays in the nominative case:

• die Ordnung
• die Nutzungsordnung

A useful tip: in German compounds, the last part usually determines the gender. Since the last part is Ordnung, the whole word is feminine.

It is a compound noun, which is very common in German.

It is built from:

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

So Nutzungsordnung is something like:

• usage regulations
• rules for use
• terms of use
  depending on context.

German often combines words into one long noun instead of using separate words the way English does.

That -s- is a very common linking element in German compounds. It is often called a Fugen-s.

So:

• Nutzung + Ordnung → Nutzungsordnung
• Nutzung + Vertrag → Nutzungsvertrag

This -s- does not usually have a separate meaning by itself. It mainly helps connect the parts of the compound in a way that sounds natural in German.

Unfortunately, there is not always a simple rule for when compounds use this linking -s-, so learners often just need to learn the compound as a whole.

Because German main clauses normally follow the verb-second rule.

In this sentence:

• Die Nutzungsordnung = first element
• gehört = finite verb in second position
• zum Nutzungsvertrag = the rest of the sentence

So the pattern is:

• Subject + verb + complement

That is standard German word order for a main statement.

It is related, but here it means to belong to in the sense of being part of or going together with something.

So gehören zu often means:

• to belong with
• to be part of
• to be associated with

In other contexts, gehören can also refer to ownership:

• Das Buch gehört mir. = The book belongs to me.

But in your sentence, gehören zu + dative means something more like:

• is part of
• belongs with

Zum is a contraction of:

• zu dem → zum

So the full form would be:

• Die Nutzungsordnung gehört zu dem Nutzungsvertrag.

German very often contracts zu dem into zum, especially in normal usage.

Because zu is a preposition that normally requires the dative case.

So:

• der Nutzungsvertrag = nominative
• dem Nutzungsvertrag = dative

That is why the sentence has:

• zum Nutzungsvertrag = zu dem Nutzungsvertrag

This is not because of motion or direction; it is simply the case required by the preposition zu.

Because most masculine and neuter nouns in German do not add a special ending in the dative singular.

You see the case change mainly in the article:

• der Nutzungsvertrag → nominative
• dem Nutzungsvertrag → dative

The noun itself stays the same:

• Nutzungsvertrag

Some masculine nouns do add an ending in certain patterns, but Vertrag is not one of them.

Because they are nouns, and in German all nouns are capitalized.

That is one of the most noticeable differences from English. So in this sentence:

• Nutzungsordnung = noun
• Nutzungsvertrag = noun

Both must begin with capital letters.

Yes, that would be a natural alternative.

Compare the two:

• Die Nutzungsordnung gehört zum Nutzungsvertrag.
• Die Nutzungsordnung ist Teil des Nutzungsvertrags.

Both express that the usage rules are part of the contract. The first uses gehören zu, while the second uses Teil von / Teil des.

The original sentence sounds very standard and idiomatic.

Yes. German allows other elements to come first, but the finite verb still stays in second position.

For example:

• Zum Nutzungsvertrag gehört die Nutzungsordnung.

This version emphasizes zum Nutzungsvertrag a bit more. It is still perfectly grammatical.

Notice what happens:

• first position: Zum Nutzungsvertrag
• second position: gehört
• then the subject: die Nutzungsordnung

That is a classic example of German verb-second word order.