The backpacking merit badge pamphlet gives a decent overview of what to expect, worth 5 minutes of your time to skim through: https://www.troop109nj.com/app/download/5844389/Backpacking+Merit+Badge+Pamphlet+2035863.pdf
None of this is magic, though. Think through what you'll need, look over the 10 essentials so you don't miss any categories, make sure to do some day hikes to break in your boots beforehand, but when the time comes just enjoy the experience and you'll probably be fine so long as you aren't grossly retarded. Sample packing lists are available everywhere.
A Sawyer mini will give you clean water. Just make sure you have a reservoir that you can hang in a tree or something to gravity-feed it or you'll hate your life. >My sleeping bag is rated 20f. Will I be fine in multiple layers of clothes and a air sleeping pad?
That's what I use even in the winter in Utah, but with heavy emphasis on the multiple layers of clothing. Put on dry clothing before bed because it'll be full of rain / mist / sweat from the day and your feet will get cold at night and then you'll feel like a zombie in the morning. Wear a hat when you sleep. Try it in your / a friend's backyard some night if you're worried. Clothes make or break your experience, think more about them.
Throw in a small flashlight just in case and pack some meals that won't require the stove. It works fine but there will be times you just don't feel like using it. Give some thought to how you will clean your dishes, even if it's just "put some cider in it and drink it."
Food for a week weights a lot, consider learning to fish. Bears also exist in some places and you should consider hanging your food so it doesn't become theirs. They pretty much leave you alone other than stealing your food, but you can bring bear spray if you want. >it's more fun if you bring a friend