Learn English – Is the sender name/signature on the bottom of a letter called ‘inscription’

The two sentences offered in your question aren't idiomatic American English (we don't say at the shelf but on the shelf), but they both mean approximately the same thing:

It's in the cupboard on {the bottom shelf / one of the lower shelves [CHOOSE ONE]}.

Down below and bottom don't mean the same thing, but the share the meaning of "in the lower part of" something.

The meaning depends on context. For example, if you're on a ship, down below means inside the belly of the ship and below the main deck (maybe in the engine room or the galley, a ship's kitchen and eating area). If you're looking for a book in a stack of 50 books on a desk in front of you, "on the bottom" means that the book you're looking for is probably one of the last 10 on the bottom of the stack rather than one of the first 10 on the top of the stack or one of the middle 30.

First, when you say:

German-American

it means your *ethnic" background is German (meaning your ancestors at some time were from Germany), but you were born in America. Or you were born in Germany but now permanantly residing in America.
This should apply to any nation specific usage.

As for:

African-American

this is more general. It could be like "European-American".

Such a person (or their ancestors) would be (or would be perceived to be) from that region of the world. I think we all know the general criteria used, but that is another discussion.