You finish PWM signal with Arduino control solenoid valve. You should use solenoid coil driver circuit. Good choice. 2 MOSFET and a few parts
No light! because of a low voltage battery. How do you increase the voltage up? You can do many ways. And, I recommend a simple step-up converter circuit using TDA2822.
I like the 12V LED. But I have only 3V of batteries. So, No light. When using this circuit, I can get light of the LED at 100 mA. And, an adjustable output voltage.