When Jaguar Paw and the villagers are being harrowed through the failed crops and dried rivers, we see the starving people looking at them in a loving and full-of-hope way, this includes the insane old man who begs them to save him. The reason for this is because they really do believe that their sacrifice will appease the gods and end their famine, which was what the priests told them.
The city is shown as collapsing from disease. Diseases often swept through places before the Europeans even showed up, spread from areas infected by the white men earlier
It is heavily implied that the priest and the king knew that the eclipse was going to happen anyways (and Mayans had advanced astronomy), highly implying that they knew it was all bullshit but went along with human sacrifices to appease the scared masses.
The children were simply left behind at the river by Middle Eye and the rest of the hunters. We never see them again, and no one mentions them. A small group of children left in a jungle populated by jaguars, snakes, and angry Mayans? Chances of survival are slim.
Without its mother around, that black jaguar cub most likely starved to death.
