Regarding pinout of PCF8574 I2C 8-bit expander
The 4-pin header J1 is what you connect to your Arduino (or other micro-controller). It has ground, power, and the two I2C lines.

The 16-pin header J2 is what you connect to the HD44780 LCD. 4 pins are not used because the unit is intended to use 4-pbit mode. The header has the same ground and power pins as the 4-pin header, because these must be passed through to the LCD. The I2C lines (scl, sda) are not on this 16-pin header.