The whole drowning Tigerlily idea was based off the Disney/Barrie Peter Pan where Hook tries to drown her but PP saves her. In Once Pan wouldn’t be doing the saving but perhaps the ordering of the deed.
As for Regina and Henry, I’m glad Henry went to see Regina. He’s at least showing care and concern for her unlike season 2 Henry. I think Regina did the right thing sending the note. She knew that Henry had other people that would look after him. She also knew she wasn’t in the best emotional place to be right now but she also accepted Henry’s offer to help rather than trying to shut him out.