C is wrong since "everyone of us have" is incorrect - everyone is singular, so it should be "has".
I'm kind of irritated with this question because "everyone of us has" is also technically incorrect -- it should be "every one of us". Oh well.
Why can't I refer "Helping" as an adj for HIM?
I may say: everyone of us has understood that without him we wouldn't....
And it's OK, right?
And then, I add an adjective to pronoun "HIM" and I am getting
...that without him helping us....
You can't use helping as an adjective because unfortunately, it isn't one. Helpful would be, but helping could never really work as as an adjective. Helping is a gerund, so if you treat it like an adjective you'll be wrong.
Your first sentence is correct because in the case of "we couldn't have done it without him,"
him is acting as a noun.
In the case of "we couldn't have done it without him helping,"
helping is acting as the noun, so
him can't do it as well. It has to be one or the other. We have to convert
him to a possessive pronoun, to connect the two nouns.