Q: "为了什么殺人?"/ "为什么殺人" (why you kill?)
A: "为了錢"/ "为錢" (for money)
为了什么/ 为什么 = for what/ why
we want to know the motive for you to do it
you do it because you want the money
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Q:"因为什么而殺人?"/ "因什么而殺人?" (you kill because of what?)
A:"因为妒忌而殺人" / "因妒忌而殺人" (I kill because of jealousy)
因为什么 / 因什么 = because of what
we want to know what is the cause of you doing it
you don't want to be jealous, but jealousy is the cause
为妒忌而殺人 sounds like you kill because you want to be jealous (of cause we understand you meant jealousy caused you to kill)
为了錢而殺人 clearly stated you do it for money
因为錢而殺人 just stated money is the cause, may be that guy you killed stole all your money and you killed him for revenge. In this case money is the cause, not your motive
Notice:
为什么殺人 put the verb 殺人 directly after 为什么
因为什么而殺人 is in a [(因 ~ 而) + (v)] = [(v) (because of) ~] structure
If someone ask you 为什么殺人(why you kill) , you can reply either "为錢而殺人" (state your motive) or "因錢而殺人" (state the cause)