Question: How does wearing the sunglasses allow the wearer to hear the speakers broadcasting the "sleep" command?
Answer: It affects the brain waves. Wearing those glasses disrupts the visual and audio signals.
Question: Why did all the police officers destroy the shantytown? And why did they beat the blind priest to death?
Answer: As part of the alien takeover, they're suppressing any resistance and discussion of the plot. They know there's a group, led by the preacher, who are onto the conspiracy and that they're somewhere in the camp. They destroy the camp to disburse them and prevent word from getting out.
Question: When Nada first puts the sunglasses on, when walking on the sidewalk, what did he see on the ground that made him realise something was wrong and different?
Answer: The glasses use a filter that makes everything appear similar to black and white television. This was not immediately noticeable to Nada until he recognized that the grate on the sidewalk appeared a different color with the glasses on (dark gray instead of bronze).
Answer: Yes, she was collaborating with the aliens in exchange for wealth and a comfortable lifestyle all along. She was playing dumb, even when she showed up at the underground meeting, a double agent.