I used the BES820 for a fair while, not a bad machine really but it does benefit from some modification.
To answer your questions:
1. The power light should flash for about a minute or so from the first start up. You should hear the pump turn on for a short time which fills the thermoblock and associated plumbing. When the power light is flashing the thermoblock is heating up. When all 4 lights turn on the machine has heated up and is ready to go. To test water temperature, press and hold the single or double cup buttons until a flow of water comes out. It should be very hot. This also will flush your group head for you which should be done before every coffee is made.
After pouring a shot or steaming milk, the lights will turn off and the power light will flash again to show that it's heating back up to temperature.
2. To program a shot volume, press the program button once when the machine is in a ready state (i.e. all 4 lights on). It'll beep once i think and the program button flashes. To program a single shot, press the single shot button once. It will begin to pour the shot and the button will also flash. Once you have the amount of coffee in the cup you want, press the single shot button again. It will stop the pour and the machine will beep twice i think, that tells you the shot amount has been programmed.
To program a double shot, the process is the same except you press the double shot button instead of the single shot button.
3. The reason it's only filling up the cup a small amount is because that's what it's currently programmed to do. By following my instructions in step 2, you can change that amount. What i actually did was to never use the program function. Because you will want to play around with the grind, dose and tamp pressures to get the best out of the machine, the machine will act differently to these changes which will require you to keep the pour going for longer or stop it sooner.
What you can do to bypass the program function is to just press and hold the single or double cup buttons (doesn't really matter which one). This will just keep the pour going until you release the button.