The sentence at hand:
I assume なんて here serves a derogatory role as など does in the following sentence:
As far as I know, the particle can be removed without significantly changing the meaning of the sentence completely or making it ungrammatical.
However, if we remove the particle from the first sentence, we have the following noun phrase.
As this is the first time seeing a question modifying a noun, this looks rather odd to me. I would have probably inserted a という or って in between.
Is this a common construct? Can questions modify nouns other than こと?
Would it also be correct to insert という or って in there? If so, how would the meaning change?
Perhaps this getting is off topic, but are my observations regarding なんて・など accurate?