Wenn die Lohnsteuer falsch ist, prüfe ich die Steuerklasse.

Because wenn introduces a subordinate clause in German, and in subordinate clauses the conjugated verb usually goes to the end.

So:

• Wenn die Lohnsteuer falsch ist = if the wage tax is wrong

The normal main-clause order would be:

• Die Lohnsteuer ist falsch.

But after wenn, the verb moves to the end:

• Wenn die Lohnsteuer falsch ist

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

Because the sentence starts with the wenn-clause, and that whole clause takes up the first position in the sentence. In a German main clause, the conjugated verb must be in second position.

So the structure is:

• Wenn die Lohnsteuer falsch ist, = position 1
• prüfe = position 2
• ich die Steuerklasse = the rest

That is why you get:

• Wenn die Lohnsteuer falsch ist, prüfe ich die Steuerklasse.

If you put the main clause first, then you get the more familiar order:

• Ich prüfe die Steuerklasse, wenn die Lohnsteuer falsch ist.

Both are correct.

Here, wenn means if.

In German, wenn can mean:

• if in a condition
• when/whenever in repeated situations

In this sentence, it expresses a condition:

• Wenn die Lohnsteuer falsch ist, prüfe ich die Steuerklasse.
• If the wage tax is wrong, I check the tax class.

So although wenn can sometimes mean when, here if is the natural meaning.

Because German uses a comma to separate a subordinate clause from a main clause.

Here the sentence has:

• subordinate clause: Wenn die Lohnsteuer falsch ist
• main clause: prüfe ich die Steuerklasse

So the comma is required:

• Wenn die Lohnsteuer falsch ist, prüfe ich die Steuerklasse.

This is much stricter in German than in English. In German, commas before or after subordinate clauses are usually not optional.

Because both Lohnsteuer and Steuerklasse are feminine singular nouns.

So their basic article is:

• die Lohnsteuer
• die Steuerklasse

Also, in this sentence:

• die Lohnsteuer is nominative because it is the subject of ist
• die Steuerklasse is accusative because it is the direct object of prüfe

But for feminine singular, the definite article is die in both nominative and accusative. That is why they look the same.

It is in the accusative case.

Why? Because it is the direct object of the verb prüfen. You are checking something:

• Ich prüfe die Steuerklasse.
• die Steuerklasse = the thing being checked

So:

• ich = subject
• prüfe = verb
• die Steuerklasse = direct object, therefore accusative

The form happens to stay die because it is feminine singular.

Because falsch is being used as a predicate adjective, not as an adjective directly before a noun.

Compare:

• die falsche Lohnsteuer = the wrong wage tax

  • here the adjective comes before the noun, so it takes an ending: falsche

• die Lohnsteuer ist falsch = the wage tax is wrong

  • here the adjective comes after sein, so it does not take an ending: falsch

This is the same pattern as:

• Das Auto ist teuer.
• Die Tasche ist schön.

After sein, adjectives normally stay in their basic form.

Because prüfe is the conjugated form for ich in the present tense.

The infinitive is:

• prüfen = to check

The present-tense forms are:

• ich prüfe
• du prüfst
• er/sie/es prüft
• wir prüfen
• ihr prüft
• sie/Sie prüfen

So in this sentence, the subject is ich, which requires:

• prüfe

Yes, absolutely.

This version is also correct:

• Ich prüfe die Steuerklasse, wenn die Lohnsteuer falsch ist.

The meaning is basically the same. The difference is mainly emphasis:

• Wenn die Lohnsteuer falsch ist, prüfe ich die Steuerklasse.
  This puts more focus on the condition first.

• Ich prüfe die Steuerklasse, wenn die Lohnsteuer falsch ist.
  This starts with what I do.

German often changes word order to highlight different parts of the sentence.

Yes, it is in the present tense:

• ist
• prüfe

But in German, just like in English, the present tense does not always mean right now. It can also describe:

• a general rule
• a habitual action
• a repeated situation

So this sentence can mean something like:

• Whenever/If the wage tax is wrong, I check the tax class.

It does not have to mean only one specific moment.

It is one noun, a compound noun.

German very often combines nouns into one word. Here:

• Lohn = wages/pay
• Steuer = tax

So:

• Lohnsteuer = wage tax / payroll tax

Likewise:

• Steuerklasse
  • Steuer = tax
  • Klasse = class/category
  • together: tax class

Compound nouns are extremely common in German, and the last part determines the gender. Since Steuer and Klasse are feminine, both compound nouns are feminine too.

Yes, prüfen works well here. It means to check, to examine, or to verify.

In this sentence, it sounds a bit like:

• checking carefully
• verifying whether the tax class is correct

Other possible verbs in German might be:

• kontrollieren = to check/inspect
• überprüfen = to check/verify more thoroughly

But prüfen is natural and correct. It suggests a deliberate check rather than just a quick glance.