does the arduino pay any attention to eeprom?
The arduino system doesn't pay attention to the eeprom, as far as I can tell. It is data memory, rather than program memory. You are free to use it to persist parameters, or last sensor readings, or whatever. Neither the build process nor bootloader docs mention eeprom at all.
This wiki page documents how to read / write in that space from your arduino program, and you can also read the atmega8 datasheet.
Note there's only 512 bytes of this eeprom on both the atmega8 and atmega168.
I might be hideously wrong about this, but I've wiped all 512 bytes of my eeprom and... so far so good. The bootloader does have code for writing to eeprom but I don't know if it currently does. A possible use of eeprom by the bootloader would be keeping a track of the number of times the flash had been written (helping you to predict when it's going to fail).
I also heard a rumour that the atmega8s prepared on the arduino boards have future winning lottery ticket numbers written in that space, so some people do a backup first.
Sorry I can't answer your other questions.