“1) Does that above mindset have anything to do with the kukuccha cetasika?”.
It is possible. However, it is more like let down feeling with a tinge of sadness, that one is still unable to get there despite one’s efforts.
“2) Can this concern/worry be extended to other sentient beings? Like “why are others not becoming Sotapanna, or sadness about others not even knowing about Buddha Dhamma, and sadness about the reality that so many infinite beings will remain in sansara”?”
Of course. That feeling (not really sadness, but metta) is in all Ariyas too.
“3) Or would worrying and being sad about others not becoming Sotapanna and remaining in sansara actually be considered as domanassa(amisa dukha) instead of niramisa dukha?”
Feeling sad about others is domanassa(amisa dukha). Of course, anyone below the Arahant stage may have a tinge of sadness too.