Is there a way to adjust the duty cycle (PWM) based upon input gained by a sensor. For example, if the sensor picks up a really high value, it would increase the duty cycle for an LED making it brighter. Can we also do this task without a potentiometer? Can all of this be done "hands-free" by the Arduino?
The example at the bottom of this Arduino reference page does exactly that. If you want to change the way the value varies, you can just modify the variables in a loop or in whatever approach you prefer instead of analogread'ing it.
There is a simple project that can be done with a photo-resistor for an analog input, a light levels sensor circuit, and an LED for an output.
The software requirement is to have a loop with a delay that reads from the analog pin the photo-resistor is attached and use that value to set the Duty Cycle for the PWM output pin driving the LED illumination level.
You can then test by shading the photo-resistor from the ambient light (I used a sheet of paper rolled up into a tube and placed over the photo-resistor on the breadboard), putting it into darkness, and by using a flashlight to provide more light than ambient in order to test the range and watch the LED dim and brighten.
I have done this project with a Raspberry Pi, which required an MCP3008 Analog to Digital Converter to interface to the photo-resistor circuit since the Pi has only digital pins. Arduino has analog pins so the ADC is not necessary.
The project that I did with my Raspberry Pi is at URL: https://github.com/RichardChambers/raspberrypi/tree/master/project08 with C source code and a link to the manufacturer of the experiment kit I am using which has the details for the actual circuit. What I did was to make the LED illumination level track to the inverse of the value reported by the photo-resistor circuit. So when the light level was low as reported by the photo-resistor then I made the LED brighter.