Who tried to use an Android device as the server that has been powered up during several months, or maybe year ?
How is the battery state if such usage ?
I think, now embedded control systems can be build basing on an Android device (also as server) + wired Ethernet LAN hosts of sensors, displays, relays...
WiFi solution i'm sure cannot be stable.
So question is about the battery life, if always powered up.
I wouldn't worry. Any decent device nowadays (and most indecent ones) have smart batteries that don't allow themselves to be overcharged. Even if the battery capacity did degrade over time from being kept at full charge it will probably only have to deal with power outages of limited duration and so should cope without problems.
Yes. No need to unplug the devices. The software also runs for months without any need for intervention. It is made of a small watchdog app and the main app. The main app closes itself every hour and the watchdog app starts the main app every minute (if needed).