“not to mention” and “let alone” are both typically used with the more difficult or unpleasant things after the phrase. The main difference is that “not to mention” is usually used to bring something new into the conversation or to imply that the thing you’re mentioning needs a whole separate conversation.

“Let alone” is a way to add emphasis when denying something. Usually phrased like “I didn’t even X, let alone Y.” Y being the thing you want to deny, X being some first step toward Y or just something related that isn’t as bad as Y.

Some examples:

“Did you kill Dave?” “I didn’t touch him, let alone kill him”

“Can you walk?” “I can’t stand, let alone walk.”

The first part doesn’t even need to be a complete denial as long as it implies the second part is impossible:

“Can you run?” “I can barely stand, let alone run.”

The EEA shows up in the list of places it does not apply. They worded it strangely, first calling out the US as a place where it does apply. Then they change it up and say it also applies to anywhere not on this specific list of places