Hi,
I can provide you with a sketch that handles 3 button inputs and 3 LED outputs, as per your requirements. During standby it will only be on the lookout for button presses and nothing else.
If I understand correctly, there will be three buttons. The buttons will not be pressed in any particular order. When the first button is pressed, the green LED turns on for 1 second or until the second button is pressed.
When the second button is pressed, the amber LED turns on for 1 second or until the third button is pressed.
When the third button is pressed, the red LED turns on for 1 second.
After this the cycle repeats.
You wil be able to easily change the duration from 1 second to any other amount.
I can provide you also with a very basic circuit diagram (3 buttons and 3 LEDs) to test out the sketch. You will be responsible to create the circuit for your scenario (including your LEDs and your LED driver)
Some additional notes based on your description:
Arduino by default only turns a LED on or off and when it is on, it is at its brightest, as far as the sketch is concerned. There are ways to dim the LED by using arduino code, but the code cannot increase the intensity of the LED more than the default.
The intensity of the LED really depends on the circuit the LED is in. Normally the brightness depends on the resistor in the circuit, however, since you have a LED driver, you don't need a resistor. The brightness is then determined by the LED driver, which is probably already set to the optimal LED output. It is correct that the LED driver, which supplies constant current to the LED, protects the LED from burning out. LEDs can burn out in a matter of milliseconds if they get too much current, so it is safer to use it instead of playing with different resistor values.
I would probably go with a 9V battery, since the arduino can take it. If it doesn't last that long you can always add another one in parallel or even a third one. You can add as many batteries as you need as long they are all in parallel.
Please note that any system, including Arduino, on standby uses power, even though this is normally very little. In your case, since you don't really need all the inputs/outputs of the Arduino Uno, you can see if you can find a smaller Arduino board which uses even less power than the Arduino Uno. Arduino has a range of boards. The only thing is that making the connections on these smaller boards may not be as easy as on the Arduino Uno, so you can still use the Arduino Uno to test it out. As long as it is Arduino, the sketch will work with pretty much any Arduino board.
The main factor for power use is your physical circuit. For the buttons you will need to use resistors for these to work properly. Since it doesn't really matter which resistor value you use, use a high resistor value as this will limit the current and therefore saving you power.