The problem is not whether Chinese allows two question words in one sentence, it's that 什么 has multiple meanings.
It can variously mean any, anything, whatever. In the example "你有什么安排吗", 什么 means "any", as in "Do you have any plans?"
This is a very similar question to "do you have plans?", which is what "你有安排吗" is.
By contrast, in the question "你有什么安排?", 什么 is asking what, as in "What plans do you have?"
Here's some examples of when 什么 doesn't mean "what":
只要认真学,什么都能学会 (as long as you study hard, you can learn anything)
他什么也不怕 (he's not afraid of anything)
他们到处放火，把什么都抢得精光。 (they set fires everywhere, and looted everything)