The way I see the heart thing, is a bit of foreshadowing. So while they're kids they mess about and play pretend with the hearts but it may be foreshadowing the current situation or a situation regarding Dess.
I think that its a case of Noelle, Kris and Dess did something at the bunker. As you need 3 codes to get in, the 3 of them would have access to all 3:
Noelle would have access to Deltarune code from the church cause of choir. Equally, Kris could have the same as the family frequented the chruch
Dess would likely have been less afraid of Carol so would have the courage to get the Pine one.
And Kris, would have access to the Cop one from Asgores time on the force.
I'm unsure if Asriel was involved but it its entirely possible
They fucked around after Kris learned stuff messing with Catti, and likely opened a dark world and as they couldnt close it Kris and Noelle get out but Dess gets lost in the Dark. This gets Asgore fired as he should have prevented this. And we are at where we are with the status quo.
Now from here its speculation with no major / confirmed foundation:
Kris loses their soul in the dark world - Not sure how but it would explain the lethargy and actions after, withdrawing and being asleep mostly. People have commented on Kris's change in the week of Deltarune with the normal playthrough in Noelle's house (her chat with Suzie)
Noelle has a pattern of hinting at repressed memories, Chapter 2 spells a bit of this out but nothing concrete. Likely she repressed the bunker dark world.
Carol gets it out of either Kris or Noelle about what happened and starts investigating herself.
This would explain the soul removal process by Kris, The obsession from Carol, and the Knight not killing Kris in chapter 3. And it adds to the speculation around Carol being positive to Kris in the normal route as she needs Kris to get Dess back as part of her plan and making Noelle stronger but compliant fits her needs in the Weird route. Carol seems like the kind of person to snap peoples necks if they do something wrong to her or the family so Kris being positively received doesn't fit that.
Off the wall shit:
This isn't Kris's first time being controlled. The bird cage and how Kris handles the soul kinda gives me vibes of that. The hatred of the soul be recognising they need it to fully function.
Likely a dark world in Mayor's office.
Gerson in chapter 4 tricks Suzie to heal by saying he pricked his finger, this to me would indicate some monsters can bleed. Also I'm not sure but Toby may have forgotten a real throwaway line in chapter 1 about being made of blood. Fundamentally, the kid could be referencing the fact that Kris is as a human made of mostly blood: Organs and veins and the like. And as he is a kid doesn't understand human physiology properly.
Gerson knew that Suzie would be at the Dark world in the Church so asked Alvin to keep his remains in the office. The lines in Chapter 2 at the grave kinda hint at that.
Things that stick out for me:
How does Ralsei know so much? Sure the prophecy can be the reason, but its unlikely that he would have access to that prior to the fountain being created so someone told him what he needed to know.
Who created the school fountain, not the abandoned class the storage room one? Its unlikely to have been created long before Chapter 1 as someone would have gone in there and there isn't a spate of missing kids.
Asgore and Toriel are loving people but kinda shit parents. They get the basics but are really neglectful in other areas. It seems the story highlights they both try to be good parents but they will put their needs ahead of their kids. Discipline, boundaries, emotional needs, basic concern around behaviours all out the window but should be red flags.
The need for "real world" money. Its an odd thread but the only use has been chapter 4 in Qc's Diner.
The eggs from the egg man. If you go full weird route, you can get a max of 2, normal nets you 4 (so far obviously). No idea on them but I think they are linked to Kris's time prior to being adopted by the Dreemurs, just based off chapter 4s egg room alone.