Checking if the email exists
You can check if the email exists by taking advantage of Amazon's 'Forgotten your password' System, just press forgot your password on the login page, and you'll be given a little box, type the email in, if it sends a recovery email, the account exists, if not, the account is locked or has been changed.

Getting an order ID
You can get an order ID quite easily, start any sort of query regarding an order and give them the item name, or a keyword of sorts, try and narrow it down so the rep believes they have the correct item, then simply turn around to them and say something along the lines of, Can you pop me the order number, so I know we're on about the same order?

Avoiding giving them the order number
As stated before, just simply get around it with item names, guess if you want, but you can also tell them that you don't know where to find it, and just stick to that story

Adding a delivery address to the account
Just simply contact the live chat, make sure it's a new, separate live chat, preferably with the 'Something Else' Category, for a newb rep.
Tell them it's not letting you add the address, so you were wondering if they could try, they'll add it to your account.

Changing the delivery address
Contact Amazon, verify the account, and then tell them that you're going to be staying with your Uncle, Father, mother, or someone else, and nobody will be home for the package for at least a week, so could they possibly change the address to help you, give them the delivery address you had added to your account.

Getting the tracking details
Contact Amazon and ask them if your order is delivered/Shipped/Dispatched, if they say yes, turn around and say something along the lines of, Could you please give me the tracking ID? I'm a bit stuck for where to find it, and I need to see how long it will be until I receive my package and when exactly during the day it's arriving?

Getting Amazon to add extra protection to the order being cancelled
Tell Amazon that one of your friends fell out with you, and they keep getting into your Amazon account and trying to cancel your order, tell them you've changed your password but if anything happens, it's not you, and ask them not to cancel any orders if your friend tries, they'll re-assure you, sometimes they don't do this, but they'll add that extra layer of protection.

Stopping Amazon from Investigating
Tell them your mother/father asked you to wait for them to get home, before you took any action, so you'll speak to them first, then come back later that night if you need an investigation, by policy, Amazon can't start an investigation without consent, however sometimes they overrule this, because they are cunts.

Cancelling Investigations
Amazon will sometimes start investigations, all you have to do is tell them you have sorted your order problem, you do not even need to specify it in detail, tell them you faced an issue, and an investigation was started, but now everything is good, and you don't have an issue anymore, so the investigation can be cancelled to stop people wasting their time.