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We report on the statistics of bubble size, topology, and shape and on their role in the coarsening dynamics for foams consisting of bubbles compressed between two parallel plates. We find that in the scaling regime, all bubble distributions are independent not only of time, but also of liquid content. For coarsening, the average rate decreases with liquid content due to the blocking of gas diffusion by Plateau borders inflated with liquid. By observing the growth rate of individual bubbles, we find that von Neumann's law becomes progressively violated with increasing wetness and decreasing bubble size. We successfully model this behavior by explicitly incorporating the border-blocking effect into the von Neumann argument. We report on bubble growth rates and on the statistics of bubble topology for the coarsening of a dry foam contained in the gap between two hemispheres. By contrast with coarsening in flat space, we observe that six-sided bubbles grow with time at a rate that depends on their size. We measure the statistics of bubble topology, and find distributions that differ from the scaling state of a flat two dimensional foam. We report on the statistics of bubble distribution and coarsening of the two dimensional surface of a three dimensional foam. The surface of a three dimensional foam obeys Plateau's laws, but does not obey von Neumann's law on the individual bubble level, although it holds on average. We measure bubble distributions