Ich kaufe Walnüsse für den Salat.

Because the verb has to agree with the subject.

• ich = I
• The infinitive is kaufen = to buy
• In the present tense, with ich, it becomes kaufe

So:

• ich kaufe = I buy / I am buying
• ich kaufen is not correct standard German grammar

A quick present-tense pattern for kaufen:

• ich kaufe
• du kaufst
• er/sie/es kauft
• wir kaufen
• ihr kauft
• sie/Sie kaufen

The singular is die Walnuss = the walnut.

The plural is die Walnüsse = the walnuts.

This is a common German plural pattern where:

• the vowel changes: u → ü
• and -e is added

So:

• Walnuss → Walnüsse

German plurals are not always predictable, so this is a word form you usually just learn as a pair:

• die Walnuss
• die Walnüsse

Because German often leaves out the article with plural nouns when speaking generally or when the exact quantity is not specified.

So Ich kaufe Walnüsse means something like:

• I’m buying walnuts
• not necessarily the walnuts

If you wanted to make it more specific, you could say:

• Ich kaufe die Walnüsse. = I’m buying the walnuts.
• Ich kaufe einige Walnüsse. = I’m buying some walnuts.

In your sentence, the bare plural sounds natural.

Because für always takes the accusative case.

The noun Salat is masculine:

• nominative: der Salat
• accusative: den Salat

So after für, you must say:

• für den Salat

Not:

• für dem Salat

This is an important rule to memorize:

• für + accusative

Here für means for in the sense of intended for or to be used in.

So Walnüsse für den Salat means the walnuts are being bought for the salad—they are meant to go into it.

This is different from some other meanings of for in English. For example:

• Ich kaufe Walnüsse für meine Schwester. = I’m buying walnuts for my sister.
• Ich kaufe Walnüsse für den Salat. = I’m buying walnuts for the salad.

Same preposition, different context.

Den Salat suggests a specific salad, often one that is already known from the situation.

So the sentence sounds like:

• I’m buying walnuts for the salad

That can mean:

• the salad we are making
• the salad we already talked about
• the salad being served

If you said für einen Salat, that would mean:

• for a salad
• any salad, or one not yet identified

So both are possible, but the meaning changes slightly:

• für den Salat = for the specific salad
• für einen Salat = for a salad / for some salad

Yes. German word order is flexible, as long as the conjugated verb stays in the second position in a normal main clause.

Your sentence:

• Ich kaufe Walnüsse für den Salat.

Also possible:

• Ich kaufe für den Salat Walnüsse.

Both are grammatical, but they sound slightly different in focus.

• Ich kaufe Walnüsse für den Salat.
  More neutral; it first tells you what is being bought.
• Ich kaufe für den Salat Walnüsse.
  Puts a little more attention on for the salad.

The original version is probably the most natural default.

It is in the accusative case, because it is the direct object of kaufe.

In this sentence:

• Ich = subject
• kaufe = verb
• Walnüsse = thing being bought, so direct object
• für den Salat = prepositional phrase

However, because Walnüsse has no article here, you do not see a special accusative ending on it. For many plural nouns, the noun itself does not change between nominative and accusative.

Compare:

• Die Walnüsse sind frisch. = nominative plural
• Ich kaufe Walnüsse. = accusative plural

The form Walnüsse stays the same.

Because in German, all nouns are capitalized.

So:

• Walnüsse
• Salat

must begin with capital letters.

This is one of the most noticeable differences from English. In English, common nouns are usually lowercase, but in German they are always capitalized.

A rough English-friendly guide is:

• VAHL-nyu-seh

A few key points:

• W in German sounds like English v
• a in Wal- is like ah
• ü does not exist in standard English; it is a front rounded vowel
• final -e in -sse is pronounced, like uh or eh depending on accent

A useful trick for ü:

• Say ee
• While keeping your tongue in that position, round your lips as if saying oo

That gets you close to the German ü sound.

It can mean both, depending on context.

• Salat often means salad as a dish
• It can also mean lettuce in some contexts

In this sentence, für den Salat almost certainly means for the salad, because the walnuts are being bought to go into a salad.

If someone meant the vegetable itself more clearly, they might specify the type, for example:

• Kopfsalat = lettuce
• Eisbergsalat = iceberg lettuce

So context tells you which meaning is intended.

Yes. The German present tense often covers both meanings.

• Ich kaufe Walnüsse für den Salat.

Depending on context, this can mean:

• I buy walnuts for the salad
• I am buying walnuts for the salad

German does not require a separate form like English am buying in everyday usage.

If you want to know which one is meant, you usually rely on context.