On my board (Arduino UNO), the free contacts have ended, and I need an extension. I plan to connect several gerkon sensors (at the output of which are HIGH-LOW), a button and an LED. The documentation states that this is a PWM controller for engines. Can it be used for my purposes? Or do I need to look for another expansion module?
As a gerkon sensors is essential a switch, and a switch is an input you need a board that gives you more inputs. That board you posted a picture of is designed to give you more PWM outputs and so is useless for what you want.