You're correct that 何も is a negative polarity item that means "(not) at all". But you seem to have missed せず is a negative verb that roughly means しないで.
せず - What does it come from?
What is the difference between the negative forms -ず and -ぬ?
JLPT N2 Grammar: ずに済む
As long as you put all your energy ...
歩けん is a variant of 歩けない ("I can't walk"). Usually a small girl doesn't use this form because it sounds a little old-fashioned or dialectal. Maybe the speaker is an old vampire or someone playing the role of it?
Is verb ending ない shortened to ん?
Verb conjugations such as 思わん、言えん
The omission of を is very common in colloquial Japanese. There is ...