Not sure if it possible in your case, but you might send and ID with it which you increase every time the button has been (really) clicked (thus not refreshed). On the receiver side, check if the ID is already received, if yes, do not execute it.
It can't be done (also, why would you think that would ever be a good idea?!)
The 8 pin chip on the ESP-01 is a 512kB SPI flash that runs at (at least) 40MHz. So to emulate that you would need:
More than 512kB of flash,
A slave SPI interface that can operate at a minimum of 40MHz, and
The knowledge, time and energy to write the firmware to emulate an SPI ...
The following may not solve of your problems, but just in case it helps...
I was using the ESP8266 both in Station mode and AP. Both worked.
In AP mode, it worked but the ESP8266 ignored my instructions to set name and password for the AP , until I realised the following
. The password must at least be 8 characters long, otherwise the instruction is ignored