Die Katze kratzt an der Tür, weil sie nach draußen will.

Because die Katze is the subject of the sentence, so it must be in the nominative case.

• die Katze = the cat
• feminine singular nominative uses die

If it were in another role, the article might change. For example:

• Ich sehe die Katze. = I see the cat.
  Here die Katze is accusative, but for a feminine noun the form stays die Katze.

So in this sentence, die Katze simply means the cat as the one doing the action.

It means scratches at the door.

The verb is kratzen = to scratch.
In this sentence, an der Tür kratzen is the natural way to say that something is scratching against or at the door.

So:

• Die Katze kratzt an der Tür. = The cat is scratching at the door.

English uses at here, and German uses an.

Because here an is being used with the dative: an der Tür.

German two-way prepositions like an can take:

• accusative for movement toward a destination
• dative for location or contact

Here the cat is not moving onto the door as a destination. It is already at the door, scratching there. So German uses the dative:

• an der Tür = at the door / on the door

Since Tür is feminine:

• nominative: die Tür
• dative: der Tür

That is why you get an der Tür.

Because der is not always masculine nominative. It can have different meanings depending on the case and gender.

For die Tür:

• nominative: die Tür
• dative: der Tür

So in an der Tür, der means the, specifically the in the feminine dative form.

This is very common in German: the article changes form depending on case.

Because weil introduces a subordinate clause, and in German subordinate clauses are separated from the main clause by a comma.

So the sentence has two parts:

• Die Katze kratzt an der Tür
• weil sie nach draußen will

These are joined by weil = because, and German spelling rules require the comma.

Because weil is a subordinating conjunction, and subordinating conjunctions send the conjugated verb to the end of the clause.

Compare:

• Main clause: Sie will nach draußen.
• Subordinate clause: weil sie nach draußen will

This is one of the most important German word-order patterns to learn.

Here sie refers to die Katze.

Since Katze is a feminine noun, the pronoun is sie.

So:

• die Katze → sie

In English, we often say it for an animal, unless we are thinking of it as female or as a pet with known sex. German, however, follows the grammatical gender of the noun here, so sie is completely normal.

Because nach draußen expresses movement to the outside.

• draußen = outside
• nach draußen = to outside / out

So:

• Sie ist draußen. = She is outside.
• Sie will nach draußen. = She wants to go outside.

In your sentence, the cat wants to move from inside to outside, so nach draußen is the correct choice.

Yes. Raus is very common in everyday German.

So you could also say:

• Die Katze kratzt an der Tür, weil sie raus will.

This is more informal and conversational.
Nach draußen sounds a bit more neutral or explicit.

Both are natural.

No. In this sentence, will is from the verb wollen, which means to want.

So:

• sie will = she wants

It does not mean future tense here.

That is an important false friend for English speakers, because English will often marks the future, but German will usually means wants to.

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

In the main clause:

• Die Katze = position 1
• kratzt = position 2
• an der Tür = the rest

So:

• Die Katze kratzt an der Tür

This is standard German word order for a statement.

It can mean both, depending on context.

German simple present often covers both English meanings:

• The cat scratches at the door
• The cat is scratching at the door

German does not need a separate progressive form like English is scratching.

So kratzt here can naturally be understood as a current action.

Yes, kratzt is tricky because of the consonant cluster.

A rough guide:

• kratzt sounds something like krahtst

The ending combines:

• tz = like the ts sound in cats
• then another t from the verb ending

In normal speech, the cluster may sound compressed, but the word is still pronounced as one syllable.

Other useful pronunciation notes in the sentence:

• Tür has a long ü sound
• draußen has au like in English cow
• ß is pronounced like s

Yes, Katze is grammatically feminine, so its article is die.

• die Katze = the cat

Even if the actual cat is male, people often still use die Katze as the general word for a cat. If you specifically want to say tomcat, German often uses:

• der Kater = tomcat / male cat

So in your sentence, die Katze is the normal word for cat.