The 5V pin can output 500mA if the bard is powered via USB and 1A if powered via the barrel jack. There is a third choice and you can get 1.5 A from the USB bus by shorting "1.5A SHORT" on the board.
The EEPROM is not advertised since it's not a real EEPROM but a flash "partition" used as EEPROM (byte addressed)