Use of 의존명사(dependent noun) "바"

Question

I actually don't use 네이버 국어사전 usually, but using another dictionary, as in here: http://dict.hjenglish.com/kr/

Here, the dependent noun 바 was explained like this:

1. Matter (I think similar to 일)(Which exists in the form of 'ㄴ/은/는/ㄹ/을 바')

Examples:

다 아는 바와 같이 --> As all knows, ...
네가 알 바가 아니다. --> Not the matters that you should know.
어찌 할 바를 모르다 --> No idea how one should do

2. Situation (A and B are bad, but I would rather choose B)

Examples:

할 말 못하고 살 바에는 차라리 죽는 게 낫지. 
--> Being unable to speak even one word, I would rather die.
어차피 쓰지 못할 바에는 버리는 게 낫다. 
--> Being unable to use, it would be better to throw it away.

3. To emphasize the speaker's stance (Exists in the form of '는 바이다')

Examples:

오인은 잘못을 시인하는 바이다. --> I WILL admit my wrongs.

The second and third one are easier to understand, as revealed in the explanations and the examples. However, I am not sure how the first one should be used, and how it differs from 일.

The Naver dictionary splits the first meaning into two:

1. 앞에서 말한 내용 그 자체나 일 따위를 나타내는 말. (The speech previously uttered itself, or speeches that show the kind of works?)

Examples:

평소에 느낀 바를 말해라.
각자 맡은 바 책임을 다하라.
나라의 발전에 공헌하는 바가 크다. 

2. (어미 ‘-을’ 뒤에 쓰여) 일의 방법이나 방도.

Examples:

어찌할 바를 모르다
나아갈 바를 밝히다
눈 둘 바를 모르다.  

Naver dictionary gave me a clearer explanation, however I still could not grasp the first meaning.

For the second meaning, please clarify how 바를 모르다 can be differentiated from 줄 모르다.

Any help is much appreciated.

Answer 1

In the first meaning, think of 바 as equivalent to 것. It's a general noun-ifier, to make verbs behave as nouns grammatically. It can be translated into English as "what" or "the thing which". If I literally translate the first examples, it'll be more clear to you:

다¹ 아²는³ 바와⁴ 같이⁵ --> Like⁵ the thing⁴ which³ all¹ knows^{2, 3}
네가¹ 아²ㄹ³ 바가⁴ 아니다⁵. --> It's not⁵ the thing⁴ which³ you¹ should know². = It's not what you should know.

This one is a little different, since it can't be translated into English word-by-word.

어찌할 바를 모르다 --> Do not know how one should behave.

Explanation: You want to say that you don't know "how one should behave (=어찌하다)", but unlike English, where "how-clause"s are treated like a noun and thus become an object of the sentence, Korean 어찌 is just an adverb and can't be used like "*어찌하를 모르다" or something like this. You need a nounifier, to take the "how-clause" as an object for the predicate 모르다. 바 comes here. By saying "어찌할 바", it's effectively a noun and can be safely taken as an object.

어찌할 바를 모르다 and 어찌할 줄(을) 모르다 are used interchangeably.