Replying to a private message.
In the third questions, the synonym of realization in the context is accomplishment (B).
Quote:
Lorraine Hansberry does not reject integration or the economic and moral promise of the American dream; rather, she remains loyal to this dream while looking, realistically, at its incomplete realization. Once we recognize this dual vision
Hansberry does not refute completely the ideal, the cause of the American dream, actually, all people might become rich and wealthy both morally and physically.
Rather she has a dual opinion or standing point on this, a dichotomy: it is true that she accepts the American dream itself and the targets it arrived, BUT at the same time she says that it does not fully realize, pick up, arrived, accomplish to its full goal (whatever it is THE goal of the American dream).
The vision of the American dream does not get the target 100%. As such, it did not accomplish its goal, fully.
Hope now is more clear