1. There are substrate calculators out there that would help you determine how much you would need to get a certain depth. Google "substrate calculator"
2. You don't need to wash it if you add it to your tank when its completely empty. I didn't wash some of mine in a tank that already had water in it and the tank got cloudy, I washed the rest and didn't get cloudy at all. You don't have to, but it will only help.
3. You can take the carbon out if you want, or since you have the prefilled pads you can leave it in because its really only effective at what it does for somewhere around 6-8weeks. But if you replace your pads know that the fresh carbon will be removing some of your ferts, that's a waste of money and detrimental to your plants.
4. Because you have heavy root feeders you should still use root tabs and all plants do better with a good fert regimen. Planted substrates don't add to the ferts in your tank, they only hold them in the substrate better so plants can access them better.
Edit: substrate calcs I found all said you'd need around 40lbs to get a depth of 2.5" in your tank. So two of the large bags from petsmart would do. Curious how you were getting 24lbs of it?