The sides of a pan provide some structural support for a cake. When the sides move a further distance away from parts of the cake batter, there is less structural support for the cake towards the center and it may fall. You can increase the structural support in a number of ways. A heating core would probably help, or you can use a stronger flour. But the easiest solution is the use less baking powder, because the carbon dioxide bubbles in the cake weaken its structure.
The raw bottoms are more of a puzzle; the 10” cake would surely take longer to bake, but I would expect the very bottom to be done quickly, and only the interior to be raw. Again, if the latter is the case, a heating core or flower nail will help with that.
If there was a whole layer underdone at the bottom, my understanding is that the failure to use bleached flour often produces an effect that looks like that.