Meine Schwester schneidet einen Pfirsich und eine Melone in kleine Stücke.

Because meine Schwester is the subject of the sentence, so it is in the nominative case.

• die Schwester = the sister
• meine Schwester = my sister

For a feminine singular noun in the nominative, mein- becomes meine.

If it were in a different case, the form could change:

• nominative: meine Schwester
• dative: meiner Schwester

So here meine is correct because my sister is the one doing the action.

Both nouns are direct objects of schneidet, so they are in the accusative case.

The difference comes from the gender of the nouns:

• der Pfirsich = masculine
• die Melone = feminine

In the accusative:

• masculine ein changes to einen
• feminine eine stays eine

So:

• einen Pfirsich
• eine Melone

This is a very common pattern in German.

The genders are:

• der Pfirsich = masculine
• die Melone = feminine

Unfortunately, you usually cannot reliably guess grammatical gender from meaning alone. You normally have to learn each noun together with its article.

A good habit is to memorize nouns like this:

• der Pfirsich
• die Melone
• das Stück

That makes sentences like this much easier to build correctly.

Schneidet is the 3rd person singular present tense form of the verb schneiden.

The infinitive is:

• schneiden = to cut

Present tense:

• ich schneide
• du schneidest
• er/sie/es schneidet
• wir schneiden
• ihr schneidet
• sie/Sie schneiden

Because the subject is meine Schwester = she / my sister, the correct form is schneidet.

German main clauses usually follow the V2 rule: the finite verb goes in the second position.

In this sentence:

• Position 1: Meine Schwester
• Position 2: schneidet

Then the rest follows:

• einen Pfirsich und eine Melone in kleine Stücke

This is one of the most important word-order rules in German.

You could also start with another element, and the verb would still stay second:

• Einen Pfirsich und eine Melone schneidet meine Schwester in kleine Stücke.

That sounds more marked, but it is grammatically possible.

Because in can take either the accusative or the dative, depending on the meaning.

Here, the phrase expresses a change of state/result: something gets cut into small pieces. That is why German uses the accusative.

So:

• in kleine Stücke = accusative

If it were about location, German would use the dative instead:

• in kleinen Stücken would mean something more like in small pieces as a state or form, not the result of cutting in this structure

Also, in Stücke schneiden is a very common fixed expression meaning to cut into pieces.

Kleine is the adjective describing Stücke.

The noun phrase is:

• kleine Stücke = small pieces

There is no article before Stücke, so the adjective has to carry the grammatical ending itself. In the accusative plural without an article, the adjective ending is -e.

So:

• kleine Stücke

This is called strong adjective inflection.

Because the idea is that the fruit is being cut into multiple pieces, not into one piece.

• das Stück = the piece
• die Stücke = the pieces

So in kleine Stücke schneiden is the natural way to say cut into small pieces.

If you said in ein kleines Stück, that would mean into one small piece, which usually does not fit the situation.

Yes. In the normal reading, it applies to both objects.

So the structure is basically:

• My sister cuts a peach and a melon into small pieces.

The phrase einen Pfirsich und eine Melone is a coordinated object, and in kleine Stücke describes the result of cutting them.

If German wanted to make it clearer that only one of them was cut into pieces, the sentence would probably be phrased differently.

Because in German, all nouns are capitalized.

So in this sentence:

• Schwester
• Pfirsich
• Melone
• Stücke

are all nouns and therefore begin with a capital letter.

This is different from English, where common nouns are usually not capitalized.

You usually would not do that here if you mean one peach and one melon as specific items.

German normally uses articles in this kind of sentence:

• einen Pfirsich und eine Melone

Without articles, Pfirsich und Melone sounds more generic, more like talking about the foods in general rather than two individual fruits.

So for this sentence, the articles are the natural choice.

Yes. In Stücke schneiden is a very common German expression meaning to cut into pieces.

You can think of it almost as a set phrase:

• etwas in Stücke schneiden

You can also modify it:

• in kleine Stücke schneiden = cut into small pieces
• in große Stücke schneiden = cut into large pieces

So this sentence uses a very standard and natural German pattern.