Now, let's check what 旗色｛旗色｝ be translated in English.
(wait to) see which way the cat jumps
The odds are in his favor [against him].
So, 旗色would imply which "side" might be a winner.
misses a something, which is the very "opponent".
Imagine when you are in the battle which flag seems to be "...
Here's the list of examples from BCCWJ.
We can see the idiom 旗色が悪い can be safely used in non-military contexts, but is always used in the context of argument, debate, competition, or at least comparison of two opposing ideas. It should not be used to describe simple failures without competitors, rivals, enemies, etc.
I feel 私の商売は大損失で旗色が悪くなった on its own ...
留まることを知らない (as I read it from meaning-book.com/): "don't know when to stop".
The meaning is more like "nobody knows how/where it will end".
But I'm not sure how to translate 1つの嘘から始まった連鎖は. (A chain that started from 1 lie?)
Your notion of the meaning is correct, but you could translate it into English as "what", as in something like "what started with a ...
する in 音がする is intransitive, and it refers to some "environmental" sound you hear. This kind of する is explained in this question. The other three are transitive. Here the subject of the sentence is 令音, and he is the one who made this sound, so 音がする cannot be used.
音をさせる, 音を立てる and 音を出す are very similar, but 音をさせる and 音を立てる are usually used with unintentional ...