Do I understand indexes correctly?
You're pretty much right but this isn't the best way to conceptualize it, rather you should draw out a Tree since that is the logical data structure typically used to hold the data within an index.
Using your notation, your first example and your third example are a little hard to distinguish between what is meant to be the key / row ID for referencing the actual row and what is the included field (but I understand what you mean, given your schema details).
Here is a good article on indexing and B-Trees which has a good example of how to conceptualize it. (You can ignore the database system specific comments, such as the section on SQLite, as the generals in this article apply to pretty much any modern relational database management system.) Additionally you can play around with this B-Tree simulator to help you visualize how they grow as data is added to an indexed table.