This is good clarification and is why I always promote Amazonn products using a store and shopping cart. I should add to this, if Amazon already knows the user (i.e. you are not logged in fully, but have the cookie in your browser that makes you recognised to Amazon) then you will get the 90 day cookie.
You can't buy it from your own link, they won't pay you a commission and rightly so. Shoemoney was being sarcastic about the short pixel in that blog post he did.
You can actually check how long a cookie lasts by viewing the cookie. If you have chrome go to Options -> Under the Bonnet -> Content Settings -> All Cookies and site data then search for Amazon. You will get a list of all Amazon cookies. You just have to figure out which is for the affiliates which would be relatively simple to test by clearing them then following an affiliate link etc. Then just click on that cookie and it tells you when it expires.
Membership means you get to make money selling to other people. It doesn't allow you a rebate for your own purchases. Otherwise, everyone would be an affiliate.
Definitely not 30 days nor 30 minutes - says right in their agreement it is 24 hours. I see no reason for them to change as it has apparently worked well for a number of years for both them and affiliates!
It is 24 hours until the customer adds the product to their basket, then it is extended to 90 days. If you use the remote shopping cart, products are added to the cart when the user is redirected to Amazon.