This game really needs a walkthrough mod. The VN mode feels buggy, like it was made as an afterthought to the free roam focus. When I reached the party scene, it became obvious I’d missed a lot—either due to branching paths, minigames, or events tied to free roam, or maybe just bad choices. It seems I should have had 20 LP with the maid before cooking for the family, which I think is connected to the shower scene I must have failed, even though I got the “look at her” moment. With the daughter, I was supposed to have met her more than once by then, but due to me ordering food instead of cooking. My LP with Kim should also be higher. There are just too many variables—this really needs a walkthrough to be fun.
I totally get how frustrating it can feel when paths branch out and you realize you've missed some juicy content. The VN mode was indeed built around the free roam foundation, but all LPs are obtained only in linear mode (VN MODE) or when you enter an event through free-roam mode, These are the points that can unlock scenes in free-roam, and not the other way around. It's not buggy.
A walkthrough mode already exists (only pro), but it will help you make decisions, but the decision about what to choose is yours, just as making mistakes is also something the player does.
Quick tip on the Marta arc without spoiling too much: You can hit that 20+ LP threshold before the Christmas event and also what happens after dinner if you nail a couple key interactions.
Meeting her early gives you +1 LP right off the bat.
Helping her out on the day she has that mishap (the burn) nets another +1.
The big one is the shower assist scene: If you get the sequence just right, you score a massive +19 LP. Mess it up a bit, and it's only +9. (The correct sequence has already been posted here by several people.)
That's why the option might be grayed; it's there to nudge you that you've got room to replay and build deeper.
Regarding Kim, I need to review it; I really don't remember.
Another important point: all the secret images have a lightbulb icon below them. This icon indicates the location of each image. (It indicates the location, but it doesn't indicate under what circumstances it will appear, so try another time of day, for example.)