Cannot spin motor 28BYJ-48 with controller board ULN2003APG
What happens if you change

pinMode(pin1, INPUT);
pinMode(pin1, INPUT); // Pin 2 ?
pinMode(pin3, INPUT);
pinMode(pin4, INPUT);


to

pinMode(pin1, OUTPUT);
pinMode(pin2, OUTPUT);
pinMode(pin3, OUTPUT);
pinMode(pin4, OUTPUT);


Answer for Q1 - Q3. You are using pinMode as an input. Using digitalWrite() on an INPUT will enable (HIGH) or disable (LOW) the internal pullup resistor on the input pin. The pin will not be able to "source" enough current to operate the stepper motor.

A4. The stepper motor has a "mechanical" 1/64 gear ratio. This is why it is hard to turn by hand.

Here are 2 pages that will help you to understand the issue: https://www.arduino.cc/en/Reference/PinMode and https://www.arduino.cc/en/Reference/DigitalWrite.