“of us” is middlemen, remove it and see the sentence…Everyone….has…because “everyone is singular.

A and C are out.

--Every single one sounds awkward/redundant. So E is also incorrect.

Finally B and D remain. Now should we go with his or him?

“his” is Object Pronoun of “he”.
“him” is possessive pronoun.

Ask question..without whose help everyone wouldn’t have succeeded?
His help or Him help?

I should say “his help”.

Katrusya wrote: Is a gerund always a noun?

I have heard the expression "helping hand" about person who helps everybody. So this expression isn't correct? It must be "helpful hand"? Because it's obvious in this expression that "helping" is an adj here.

I think "helping hand" is a correct expression in that helping is NOT used as a gerund but as a present participal modifying the hand, similar to phrases such as "dying soldier", "working class", and "moving bus"...

but the meaning differs between "helping hand" and "helpful hand".