Hmm, let's tackle these one at a time.
1. Serena's journal hint is actually just trash. I forgot to update it, so feel free to ignore it. If you have unlocked Spa research for the club, you have all of the available research options for now. If not, follow the main storyline (your character's hint).
2. What does Natalie's hint say? She has to be non-virgin if you want to see any beach sex scenes. If you still haven't progressed far enough in her story to have sex with her, you'll have to do that first.
3. Hmm, some people have complained before about not being able to recruit Catherine. Maybe it's bugging out again. If you're on Discord and feeling like it, join my server and send me your save file via a DM and I can troubleshoot this and the other issues for you :D