ようーのない
So I was watching a show and I encountered a line that used a grammar pattern that I've never seen before.
The original sentence was:
避けようのない滅びも、、嘆き、全て君がが覆せばいい
I understood the rest of the sentence, but what really confused me is the first part:
避けようのない
From what I looked like, this seems to mean, "impossible to avoid".
This word is a combination of the volitional form of 避ける, a の particle, and ない（ある's negative form)
So my 2 questions ares:
#1: Does this really mean, "impossible to avoid", or does it have a different translation?
#2: If my translation is correct, does that mean that every time you put a verb in the volitional form and add のない, it adds the meaning of, "impossible to"?

Question

ようーのない
So I was watching a show and I encountered a line that used a grammar pattern that I've never seen before.
The original sentence was:
避けようのない滅びも、、嘆き、全て君がが覆せばいい
I understood the rest of the sentence, but what really confused me is the first part:
避けようのない
From what I looked like, this seems to mean, "impossible to avoid".
This word is a combination of the volitional form of 避ける, a の particle, and ない （ある's negative form)
So my 2 questions ares:
#1: Does this really mean, "impossible to avoid", or does it have a different translation?
#2: If my translation is correct, does that mean that every time you put a verb in the volitional form and add のない, it adds the meaning of, "impossible to"?

Answer

uchyさん。
"impossible to avoid" and "There is no way to avoid." are almost the same meaning.

Answer

I think that "避けようのない" means "impossible to avoid".

Answer

#2: 
× that mean that every time you put a verb in the volitional form and add のない     ← wrong
As AKIさん mentioned  → 連用形 + ようのない
連用形：continuous form; second base; continuative base
Volitional form：意思
逃れ's  volitional form is 逃れよう, but this "よう" doesn't mean 意思, it's 様(state, situation, or etc.).
Here is ようがない/ようもない's grammar page of the site.
https://learnjapanesedaily.com/japanese-grammar-%E3%82%88%E3%81%86%E3%81%8C%E3%81%AA%E3%81%84%EF%BC%8F%E3%82%88%E3%81%86%E3%82%82%E3%81%AA%E3%81%84-youganai-youmonai.html
Examples：
避け ようのない　　There is no way to avoid.
逃れ ようのない　　There is no way to escape.
知り ようのない        It's impossible to understand.
書き ようのない        It's impossible to write.

By the way,
Is the sentence from Kyubey?
If so, 避けようのない滅び's nuance is like a "the fixed perish/doom".

Answer

Yes, 避けようのない means "impossible to avoid"

The structure is: 
避け: a noun, "avoiding", which is made from the 連用形"避け“ from 避ける
よう (様）: a noun, "appearance/situation/way/method", 
の　： a particle for possession.
ない: "don't exist"

Literally: No existence of method to avoid.