The CLKPR is a non-volatile EEPROM type register; once its value is changed, it remains there until it is altered again.
According to the ATMega2560 data sheet, CLKPR is a standard read/write register, except that a special procedure is required to change its value.
The CKDIV8 fuse determines the initial value of the CLKPR register upon reset.
I wrote to those EEPROM registers which do not exist
Which "nonexistent" registers, exactly? Post the EEPROM write code that causes the problem.