] It can't be that Darcy pushes Giorgiana or will push her to marry Bingley, especially at the time when they left Netherfield,

I didn't mean to imply that this was something that Darcy wanted now. In fact, I specifically said it wasn't.

] b/c Bingley's connections is below Darcy's own and he is very strict in that matter and will not give up his concerns of good relations (BTW, these things I like very much about him), also at that time he was struggling with himself not to fell in love with Lizzy whose relations' condition in life is so decidedly beneath his own, so how can he accept the same thing for his beloved sister?

(At least) two reasons. First, in his situation, connections are probably more important to him than to Georgiana in hers. (For example, those connections will be the grandparents, aunts, uncles, etc., to the heir to Pemberley.) Second, I think his main concern for Georgiana is that his shy, sheltered sister marry someone who will be kind to her, and who isn't after her money. He gets both of those in Bingley.