There's no way that Darcy could have known that he would find Elizabeth alone that morning. She was going to walk down to the church with her aunt and uncle, and only stayed behind because she got Jane's letters and wanted to read them. I think he was just set on calling on them--all of them--and continuing to show them every attention he could, and to spend more time with her if possible.
As for the issue discussed lower down, of Darcy realizing that he still wanted to marry her within about half an hour, well, it's not like Lizzy first led him on and then purposefully broke his heart. She never encouraged him to fall in love with her, and really only said the things she did at Hunsford under great provocation. That doesn't mean that she wasn't wrong in what she said, and more substantially, wrong in her opinions, but Darcy, being the gentleman he is, has forgiven her that. But like I said, it's not like she broke his heart on purpose or anything.
As for the issue discussed lower down, of Darcy realizing that he still wanted to marry her within about half an hour, well, it's not like Lizzy first led him on and then purposefully broke his heart. She never encouraged him to fall in love with her, and really only said the things she did at Hunsford under great provocation. That doesn't mean that she wasn't wrong in what she said, and more substantially, wrong in her opinions, but Darcy, being the gentleman he is, has forgiven her that. But like I said, it's not like she broke his heart on purpose or anything.