The process of ionization of the donor is temperature dependent. Since here one deals with a large number of atoms statistical physics is applied. At high temperature the fraction of donors ionizing is large compared to unionized donors. The process of diffusion makes the ionized electron move to the p-region thus creating the depletion region (similar conditions hold for the n region with holes migrating). Coming to your question as to why electrons are not captured by the positive ions formed in the depletion region they are in fact but thermal energy leads to dissociation. To answer your second question note that the E field formed in the depletion region points from the n-region to the p-region and thus support the movement of negative charge from the p-region to the n-region.