Hey Vanessa,
I use to do the 2.4km for army BFA training. The warm up is important to practice as they will most likely warm you up when its time to run the test. If it's anything like the army though it will be just running around in a 20 meter circle for a minute or two and some stretching, then the run. I use to practice that before my run.
For the actual run i usually practised just around my home. Sounds like you have a 2.4 km course mapped out already? Does it go over hills or any slopes?
As said, forget the treadmill, it's detracting you from your goal. In fact just about anything will detract you from it besides lots of 2.4km running. So do that as much as you can.
Are you jogging/running the whole distance or stopping to walk any part of it?