Where can I see the full key-to-character mapping for a language-specific keyboard?

The Ukelele app suggested in this answer can give you a printout of the keyboard layout for every combination of modifier keys in the form of keyboard diagrams (not a list unfortunately). The resulting diagram looks like this:

Follow below steps to get a diagram:

1. Install and open Ukelele, you're greeted by the main window:
2. Open System Preferences → Keyboard → Input Sources and select the input source for which you want an overview. Alternatively select it in the menubar:
   
3. In Ukelele go to File → New From Current Input Source, this creates a copy of the keyboard layout:
   
4. Double click on it to open the keyboard layout in the main window.
5. Press the Print button in the top right corner:
   
6. Actually print the overview or save it as a PDF (through the PDF dropdown in the lower middle of the print dialog).
7. Repeat step 2 to 6 for any other input sources you need.

Use Keyboard Viewer instead of the preferences pane.

Use the Screenshot app found in Applications/Utilities to create shots of the different modifier levels.

I don't know of any easy way to get the Unicode numbers. Perhaps the Ukelele app, which can make a copy of the current input source for analysis.