connect the first pin of the PCF8574 to the VSS of the LCD, 2nd pin to the VCC and so on. The input pins of the PCF8574 i.e. SCL and SDA should be connected with the SCL and SDA of the microcontroller.
ADC is used by most of the sensors for eg- temperature sensor, force sensor, IR sensor, potentiometer, and many more. All these sensors send the data to the microcontroller in analogue form, which then converts it into digital values.
The process is very straight forward, you have to measure the number of times input pin goes high and low in 1 second. This measure will give you the frequency. 1.) Set a pin as input and make sure you connect a pull-up register to it. Pull-up is necessary otherwise pin will not go to high state. 2.) Give in the frequency input to the pin and display the frequency on the serial terminal via UART.
let's say I want to display '1', so I can do that by turning on segments 'b' and 'c' (you can also turn segments 'f' and 'e' on). To display '5', I have to turn on 'a', 'f', 'g', 'c' and 'd' and so on. That's all you need to know for seven segment display. It's very simple and used widely.