1

I read this,

What she wouldn’t have given for a weapon, even a measly screwdriver to protect herself with — anything other than this useless foot and slight silk gloves.

I search this pattern and find another

What he would have given for a single day of calm.

I almost can guess out the meaning of this sentence. But I can't understand the gammar. Why does "what" start a non-question sentence?

2

Because this construction is, in origin at least, a rhetorical question.

What wouldn't Napoleon have given for an extra battalion of troops at Waterloo?

with the implied but unstated answer "Anything at all."

In general the meaning is "X would have greatly desired Y at a particular moment -- it would have turned disaster into victory". This is expressed as "What wouldn't X have given for Y?" or "What would X have given for Y?" inviting the reader to supply the obvious answer to the rhetorical question.

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