It starts with finding the page: Amazon -> Customer Service -> Search for "personal data" -> Search result #1 is "Request Your Personal Information" which nicely explains what to do and links directly to that page.
The need to verify or activate a data request via clicking a link? Of course required so some third party can not just request your data to your inbox (and process it along the way) without you actually wanting to do that.
All the mentions that most of the data is available in your Amazon account? Well, what many people are looking for (order history etc) is and even nicely formatted, searchable and cross linked to make it much more convenient.
Clicking "Remove address" only removes it from the list of addresses? Of course, addresses you ordered to in the past can not be deleted as they have to legally be stored together with other order information.
And the list goes on and on.
I get that it is scary that a big company keeps all the data you gave to them. And it is also unfortunate for you that it is not their business goal to make it instant and pretty for you to look at all the data. But there is no reason for them to do that.
If you don't want Amazon to have your data, don't user Amazon. When you use Amazon, the way you can get a lot of data from them is actually pretty good (also compared to other companies which pretent search history does not exist and so on).
(And bye to some Hacker News points. This will get nicely downvoted I suspect.)