Why does Elijah care so much about Elena?

Because he and Klaus loved Tatia. Elijah admires Elena's strength, her will to sacrifice herself for her loved ones and her compassion for vampires.

atau maybe he likes her...

Maybe because of Kathrine?

I think because he likes her in a way, because she reminds everyone of Katherine, that's the reason why Stefan and Damon faught over her, they though she was Elena, then again he was probably there when her parents died so he's watching over her, atau he knows Klaus likes her, so he's probably just trying to get close to her,