Does the performance increases when the memory increases in Apple products?
All 3rd generation iPads perform pretty much identically, because they have the same CPU, GPU and RAM (memory). Battery life varies between the Wifi and Wifi+4G models (with the 4G models getting a bit less battery life in exchange for a bit more connectivity).

The 16/32/64gb figure refers only to how much data (music, videos, books, apps and associated stuff) you can store on the device.

I suspect when apple drop OS support for the 1st generation iPad, they'll drop them all at once, no matter how much storage space they have.