Faucet valve control
There are several different types of valves available.  You have already discovered solenoid valves - most common are Normally Closed but Normally Open and combination Normally Open &amp; Normally Closed are also available.

There are also motorised valves available.  Again - you can fabricate your own using a large hobby servo positioner attached to a ball valve or purchase one ready-made.

Detecting water level is possible using any of several different techniques.  You can fabricate or purchase float switches or measure the weight of the water in the vessel or use conductive probes to detect the presence of water.

You will find float switches in most dishwashers and water weight sensors in clothes washing machines.

Your best bet going forward is to research some of these options, then return here and modify your question with more information.  We will help.