I don't quite understand the 「など」in this sentence

彼の精神は崩壊寸前なので、いつ助けるべきかなどと時期を図っているどころではありません。
His mental state is on the verge of collapse, so this is no time to be seeking the right moment to help him.

Is it similar to なんて? Like: “This not time to do such a thing as A”?

Also 「など」is paired with the particle「と」, is it an adverb marker, or is it quoting?

It’s as you say, なんて is the colloquial contraction of などと. The と is for quotation, it wraps the idea expressed before など and passes it to 図る as the thing being taken into consideration.

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