I promised some more explanations, so here goes:
Part I
名を知られなかった - [spoiler]this is 知られる[/spoiler] - Jisho.org - “his name was not known”
~ておりました - this is the same as ~ていました (see 居る - Jisho.org). It is used for various reasons, e.g. to indicate old man’s speech, to indicate humbleness, and it is even used in some dialects.
幾人となく - [spoiler]https://jisho.org/search/となく[/spoiler] - maybe something like “how ever many people”?
しばらく休もうといたしまするうちに - here we have a nice collection of 3 grammar points 
Let’s pick them apart for a bit:
- いたしまする - this is an old conjugation of the verb いたす which is a humble form of saying “to to” regarding one’s own actions. So it basically means the same as する.
- 休もうとする - to try to, to be about to. See https://japanesetest4you.com/flashcard/learn-jlpt-n3-grammar-ようとする-you-to-suru/
- うちに - while (some condition holds whose duration is not known in advance). See grammar - Difference between 前に and うちに - Japanese Language Stack Exchange
Part II
いつともなしに体が連れてきました - [spoiler]See https://learnjapanesedaily.com/japanese-grammar-ともなく／ともなしに-tomonaku-tomonashini.html[/spoiler] - without knowing when / without realizing, my body got tired.
眠っちゃならない - casual contraction of 眠っては - must not sleep
我慢をしていなくちゃならない - casual contraction of いなければ - must endure
For more information on casual contractions please see this excellent forum post.
麻酔薬をかがされた - causative passive form of 嗅ぐ (to sniff) - was made to inhale
Part III
頼みを聞いてくれぬか - ぬ is an old form of ない, so this is the same as くれないか or くれませんか
頼まれれば - [spoiler]The ば-form has the meaning of “if”. See Conditionals – Learn Japanese
やらぬわけにはゆきません - Again these are two points mingled together a little bit.
- ゆきません - this is an alternative spelling for 行きません
- やらないわけには行きません - [spoiler]I have no choice but do (due to circumstances outside of my control). See My Grammar Mastery - Kanshudo
またたくまに - This should be more understandable in kanji: 瞬く間に - in the time of a blink. This is a very common construction that comes in all shapes and sizes, e.g. ああという間に - in the time it takes to say “aaa”, or (as you will see later in this story) 見る間に - while watching. Also the verb 間に合う has the same root - to meet in time.
Hope this list helps you a bit, and happy reading!