Q:

 Is it possible to write to the flash memory while at the same time executing code from flash?

A:

 On devices with less than 512 KB flash it is not possible to read from the flash (execute code) while it is being written/erased). When writing to the flash memory in these devices the code must be executed from SRAM.

For devices with 512 KB flash or more you can write/erase to the lower half of the flash while reading from the upper half, or vice versa. Reading and writing/erasing from the same half simultaneously is not possible.