Electrical – Solenoid Valve will not open

A solenoid is certainly the cheapest and easiest thing you can make yourself. Plus, it's not difficult to direct the flow of the water this way. You don't even need to make a valve. All you need to do is to re-direct the flow of the water.

Since you have a flexible tube, you simply need to move the end of the tube between two positions. In one position it squirts the water down, and in the other position, it squirts the water into a drain.

You can wind the solenoid coils yourself. Just cut lengths of steel rod, and wind coil wire (enamelled copper wire around them).

Push the end of your water tube into a short length of steel tube. The springyness of the water tube will hold it away from the solenoid, and allow water to flow into the drain (This is also the fail safe position. When the power fails, it will drain). When the solenoid is energised, it will attract the tube, and allow the water to flow down and be seen.

You may find that the flexible tube doesn't actually work well as a spring. In that case add a spring. Or, use a fairly long piece of thin steel tube instead of the flexible tube. This will be flexible enough to move the approx 4mm required.

Modules like the ESP8266 which have no on-board regulator but do need a regulated power supply. Indeed, a power supply voltage that is too low will cause the module to reset.

What I would do in your case is get a boost module like this one to convert the voltage from the batteries to 3.3 V. On the module there's a trimmer to set the output to 3.3 V, set this BEFORE connecting the ESP8266 because such an upconverter module can easily generate 12 V which would fry the ESP module !