Learn German: Du brauchst die Kerze für die Behandlung nicht zu kaufen. - You do not need to buy the candle for the treatment.

In English, we say "you do not have to" or "you do not need to". In standard German, when you want to express that something is not necessary, you use brauchen + nicht + zu + the infinitive verb. While Du musst die Kerze nicht kaufen is understood, brauchen ... nicht zu is the most natural and grammatically elegant way to say "you don't need to" or "you don't have to".

Why is nicht placed right before zu kaufen instead of earlier in the sentence?

In this semi-modal construction, the action verb (kaufen) goes to the very end of the sentence, just like it would with a normal modal verb. Because nicht is negating the action of buying the candle, it is placed right in front of the verb phrase it negates (zu kaufen).

I see für die Behandlung. Which case is being used here?

It is in the accusative case. The preposition für (for) is a strict accusative preposition; it always forces the noun that follows it into the accusative case. Because Behandlung (treatment) is a feminine noun, the article remains die, which looks exactly the same in both the nominative and accusative cases.

Can I leave out the zu and just say Du brauchst die Kerze nicht kaufen?