#1) This recently happened to me. I quite inadvertently found out that a very close friend, all the way back from and through high school, had lost one of her adult sons last year (in his 30's). We had only communicated a few times over the years.
I felt really bad for her, so I posted a note via a Classmates account telling her how heartfelt sorry I was, and I could not imagine the pain she must be feeling. Told her to reach out to me anytime. About three weeks later I received a long email from her, telling me how great it was to hear from me. She felt a bit isolated as she is divorced, and her other adult son has his own family, so no one home.
We have now been exchanging emails quite regularly, catching up on 40+ years. So in the end I think it was beneficial for both of us.
#2) Tough question. I have two close adult children, and an extended family by relation and marriage. So I am grateful to have a solid support system already in place. But I am a private person on a few levels, so just "We are here if you needs us." would be nice to hear.