(2) By adding carefully tuned Gaussian noise. In the last 6 years we have also figured out how to add much less Gaussian noise: "The 2020 Census Disclosure Avoidance System TopDown Algorithm" https://arxiv.org/abs/2204.08986
(3) This one is harder to answer, since the Census Bureau aimed to release the same style of statistics as in previous decades. So the goal of 2020 was to release the same statistics with the same error bounds. Evidence suggests they succeeded in doing this. "Evaluating Bias and Noise Induced by the U.S. Census Bureau's Privacy Protection Methods" http://arxiv.org/abs/2306.07521, "Evaluating the Impacts of Swapping on the US Decennial Census" http://arxiv.org/abs/2502.01320
(2) By adding carefully tuned Gaussian noise. In the last 6 years we have also figured out how to add much less Gaussian noise: "The 2020 Census Disclosure Avoidance System TopDown Algorithm" https://arxiv.org/abs/2204.08986
(3) This one is harder to answer, since the Census Bureau aimed to release the same style of statistics as in previous decades. So the goal of 2020 was to release the same statistics with the same error bounds. Evidence suggests they succeeded in doing this. "Evaluating Bias and Noise Induced by the U.S. Census Bureau's Privacy Protection Methods" http://arxiv.org/abs/2306.07521, "Evaluating the Impacts of Swapping on the US Decennial Census" http://arxiv.org/abs/2502.01320