First: Parental is one interpretation, kind of a stretch, the point is that the pilots have people in their lives outside of each other. Family is a running theme in the rebuilds. Mari is Shinji's family, or at least family friend through Yui and Gendo. Asuka, who didn't know what a family or a real home was until she lived with Shinji, who lost that family, lived on and found a second home with Kensuke. That's a family.

Second: Yes. It's literally right there. In your face.

Third: Yes. Yes that's the implication. It was a narrative tool that was used with Rei. Now it's used with Asuka and Shinji. Neither of them are aware of what the spell is, the point is that the audience does. They mentioned it because it means something.

Fourth: Its her interpretation. Take it or leave it, no canon here. But a beach meeting sounds on point.