What are the adverb + 何 +を doing in the following sentence?

Question

In this book I'm translating, the narrative character is told the following line of dialogue by a girl before the sentence I'm asking about (bolded below).

「あなたには、生まれついての才能があるのよ 人を殺す才能。 生き残る才能。 暗殺者としての才能が」

呆れた話だった。いきなり何を言いだすかと思えば。

I've already translated the above, but I don't know what the syntax for いきなり何を is. I recognize いきなり as a adverb followed by 何 then a particle. Yet because I'm unable to recognize what is affecting what, I don't know if I should translate いきなり何を as いきなり何 followed by を (resulting in adverb - what - を - verb), OR treat the adverb いきなり as if it's separate from 何を (which translates the sentence to adverb - verb - what- を - context in English).

Possible translations for いきなり何を言いだすかと思えば。 I've come up with are

Without warning immediately after what she said I start talking.

I start talking at the thought of her words without warning to what I say.

Without warning to what I say I begin to speak immediately after her.

Constructive criticism that helps me understanding the correct parsing of いきなり何を is appreciated.

Answer 1

• いきなり is an adverb meaning "out of nowhere", "all of the sudden". Forget "without warning" for now. It plainly modifies 言い出す as an adverb. 言い出す is the first verb after いきなり, so it cannot be simpler.
• 何を is "what". 何 is the object of 言い出す.
• 言い出す is "to start saying", "to bring up (a topic)". Its subject is the girl.
• か is the question marker.
• と思えば is the plain old quotative particle followed by a conditional form of 思う, whose subject is the narrator. 思えば is usually called "conditional", but it can also describe a trigger of a succeeding event ("and" or "but").

いきなり何を言いだすか
What (the heck) is she talking about out of nowhere?

「いきなり何を言いだすか」と思えば…。
I wondered what she was bringing up out of nowhere, and/but...

The remaining half of the sentence is left unsaid, but it should be something like "what she said was even beyond my imagination".