I would add, why do certain particles decay into other particles? For example, the tau particle contains nothing else, as far as we can tell, yet it decays into certain other particles (and not the same ones every time).
More generally, the standard model records a lot of particles and things that happen, but not why those instead of others. I suspect there's a simple model underneath, but I have no idea what it is.
As a physicist I'd say these things are well understood.
- Why do certain particles decay into other particles?
Quantum mechanics is totalitarian: what ever is not forbidden is mandatory. Forbidden: excluded by some symmetry principle (violation of a conserved quantity, like energy, angular momentum, ...)
- The tau decays into certain other particles (and not the same ones every time).
Tau carries electric charge, fermion number, angular momentum. The decay products' total quantum numbers match that of the tau. But the quantum-mechanical totalitarian principle says that every possible combination that satisfies that constraint happens with some amplitude.
- The standard model records a lot of particles and things that happen, but not why those instead of others. I suspect there's a simple model underneath, but I have no idea what it is.
If by 'those' and 'others' you mean all the varied observed phenomena, then yes, there is a simple model underneath and it IS the standard model. If by 'those' and 'others' you mean 'why is the SM the way it is', that's (likely) an out-of-bounds question for the SM in the first place. But a modern perspective on the SM is to think of it as a low-energy effective field theory anyway.
More generally, the standard model records a lot of particles and things that happen, but not why those instead of others. I suspect there's a simple model underneath, but I have no idea what it is.