The reionization epoch can be determined using mostly low angular polarization data. The detailed physics is actually rather drawn-out, but basically it relies on the fact that there is some probability that radiation will be rescattered off these newly ionized regions in different ways than in the unionized regions. The anisotropy of the two sides of reionization (known as the optical depth of reionization) is a parameter value in most fitted models for polarization. As the WMAP results proport to give new and better constraints on polarization, we therefore have better constraints on the epoch of reionization.

Also, it isn't quite right to say that flatnesses was assumed. We can actually get at flatness independently using one other cosmological measure. This could be either in the form of a correlation function from redshift surveys, from mass measurements from lensing, or any number of other "parameter degeneracy breaking" measurements that can be made. Once this is done, the Omega_total (the overall "flatness" parameter) is measured to be 1.02 +/- 0.02 or nearly flat. Since it is shown to be so close to flat assuming flatness and going from there is the best way to fit the data. There are games that are played assuming the universe to be as far from flat as possible and, though the fits aren't quite as good, they are still in the same area for the other parameter measurements.