I've never done this so here it is off the cuff .... make the following script into an application (it will launch full screen)
#!/usr/bin/osascript
tell application "APPNAMEHERE"
activate
tell application "System Events"
keystroke "f" using {command down, control down}
end tell
end tell
make a plist like the following in launchagents for the user
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
<key>Label</key>
<string>org.yourname.yourapp</string>
<key>ProgramArguments</key>
<array>
<string>open</string>
<string>-a</string>
<string>/HIDDEN/FOLDER/PATH/TO/LaunchFullScreen.app</string>
</array>
<key>RunAtLoad</key>
</true>
<key>TimeOut</key>
<integer>120</integer>
<key>EnableTransactions</key>
<true/>
</dict>
</plist>
...as for locking the app in full screen... I don't know how to do this, maybe check out https://developer.apple.com/documentation/coregraphics/quartz_event_services#//apple_ref/doc/uid/TP4... - use this to limit window/mouse movement so they can never actually move the mouse to the area of the screen that minimizes / disables full screen. Then disable keyboard shortcuts. Check out BetterTouchTool ...
i know keyboard shortcuts are stored in a few different plists, but to the best of my knowledge there's a lot to do if taking that route...
other thought is open the application within a self made application that limits everything you need limited
hopefully someone else can chime in that has successfully done this.
