The content of a new EEPROM is unpredictable, all locations should be set to $FF but this cannot be guaranteed. It is simple to bulk erase an EEPROM with your PIC programmer (always assuming your programmer is capable of handling EEPROMS).

If you write to the EEPROM, the content is retained even with the power removed.

Yes you can have as many interrupts as you want, but your program becomes more complex.