] was thinking of why Wickham singled Lizzy for his inquiries about Darcy? Is she the only one of the party who noticed his greeting to Darcy,and he noticed that?

Wickham ended up at a card table between Lydia & Elizabeth -- and that could have been Lydia's maneuvering as much as Wickham. Lydia was very involved with the game, which gave Elizabeth & Wickham leisure to talk. I don't know if Wickham necessarily singled out Elizabeth for the details about Darcy; he might have asked one of the other Bennet girls if had been seated by them and they had leisure to talk. So part of it is just happenstance It is certainly possible that he noticed that Elizabeth actually saw his reaction when he met Darcy, however, and thought she would be the best person with whom to test the waters, so to speak.

] or did he notice from Darcy's eyes that he cares about her and tries to take her in his side as soon as possible before Darcy does so.

I don't think Darcy's admiration for Elizabeth would have been apparent enough for Wickham to notice it. There would not have been enough time, since Wickham & Darcy saw each other and reacted so quickly -- after that, I don't imagine Darcy even looked at Elizabeth, and the narrator tells us that he was trying not to look at her before he saw Wickham.

] Also I wonder why Lizzy is so curiose to hear about Mr. Darcy from him. I think inside her heart she cares about Darcy more than W whom she knew for a very short time.