Too many questions for one post :)
1. You can use your "custom" whatever even in the category template, too.
2. Yes, replace it. Kinda. Page templates and category templates serve very different goals, so basically it will be "replaced" in its use.
3. Forget the Page. A Page can NOT use a category template - that's nonsense!
4. If you get out the word "Page" from your mind - we will have a very quick understanding.
Despite what you think, when you click on a category name - what is displayed is the "archive" or that single category. Just don't create any Page. Category archives can be displayed by different template files according to the Template Hierarchy.
And finally, to quote you: "I am not sure" you read the article at the link I gave... before replying.