1. Generally, the JREs should be interchangeable (unless you're using some extensions specific to given JRE and not really being part of the JRE standard). So while technically possibly the Azul JDK might work as well, probably nobody tested the add-on with it and it's not on the recommended list so if something breaks, you're on your own.
2. I'm not familiar with this particular add-on but you typically only need JRE on the component where you run your modular inputs. Just as with DBConnect, I'd expect it to be just the HF.