He starts talking to Shinji because Shinji is cute & likeable, and a Lilin, and he likes Lilin. What other reason is needed?
I'll sooner or later make my full thread explaining the Kaworu x Rei plotline and how important it is.
True, Shinji is likeable. The rest of what you said might or might not make sense (well, I do think the lake scene has to have Angels in there too), so I'll wait for your thread.