1) The implication is the daughter's friend was the one sleeping with Frank, since she mentioned she borrowed the necklace and had also told her parents she thought her friend was pregnant and that's why she was acting weird. I assume it's the same person that had called Frank during the game and maybe just used a different name? I think all the Nick stuff is real but I find it strange that she wouldn't have slept with Nick if her dad didn't pick up the phone (maybe it's because the friend then took another pregnancy test or something so she got suspicious?)
2) Yes they definitely were, since the earrings she was wearing that she claimed to have bought for herself were the ones that she had gotten from Frank. Nothing changed about their relationship except that she realized Frank was also seeing someone else on the side since the earrings/necklace were a matching set.
3) I just assumed that it wasn't related to the revelations but just to show how much they went back to their separate lives on their phones and how disconnected they were as a family from each other.
4) I don't think they're necessarily saying mixed race friendships can't work, but that Logan as the only POC in a white friend group always felt that he was trying to fit in more because he already knew he was different (it goes back to the same thing about his job, about how they already didn't trust him because he was black, but being black AND gay was a step too far). And that the rest of his friends didn't even realize the white privilege they had and how different their lived experience was from his because of how shallow and self absorbed they were.