Is there any stuff stored in the EEPROM initially, that I shouldn't overwrite? Can I start storing data at location 0?
It's all yours! Nothing written there by default.
255 is written in all eeproms by default
When I did EEPROM.read(0); I got 105..and I didn't mess with this prior.
Probably something left over from a prior experiment or test. EEPROMS should erase to 0xFF. The Arduino does not use any of the EEPROM; it is all available for the user.
So just to make sure the arduino will never use EEPROM itself?
Well, "never" is a long time, but at present, it's all yours.