CPU cannot run without power!

You need to have a "power souce" for the CPU to finish saving the data into EEPROM.

one way to do it is to have a rechargable battery (or a big Cap.)to supply the CPU and EEPROM (and those chips involved).
Use a power down sensing circuit. When power down, generate an interrupt and have the CPU write to the EEPROM. Than the CPU switch itself off or in sleep mode.


The other way is a bit tricky. This works only if your circuit works in a wider voltage range, say 3-5V for example.
Use a power suprevisor chip which generates interrupt at say 4.75V. Provide that you have enought energy stored in your power supply circuit, your CPU should save the content to the EEPROM.

For the 4th point not sure what is your question.

Hope this can help...

Lawrence :-)