Linux

I did't know much about the German keyboard layout but I know the Czech one, which is derived from it (we both use QWERTZ) and was able to look up most of what I didn't know.

So, the keyboard has 4 layers: default, Shift, AltGr, AltGr+Shift (the fourth one is not standard but is recognized by xkb; in Czech I use it for custom character mappings, in German it is standardized but Linux-only).

• Default layer prints lowercase letters a-z and äöüß, numbers and the symbols in the lower-left of each key.
• Shift layer prints uppercase letters A-Z and ÄÖÜ and symbols at the top left of each key.
  • Caps Lock only affects letters.
• AltGr layer prints lower-right symbols, most of which are only populated in a later version of the layout.
• AltGr+Shift (Linux only) prints upper-right symbols.

As you can see, AltGr+2 produces ², and AltGr+3 produces ³. I think the full-size "2" and "n" are misprints. My old Czech keyboard has some errors too.

By the way, Czech is more chaotic:

• we have lots more diacritics so the number row only prints numbers on its Shift layer (most people therefore use the numpad only)
• to print rare diacritics (ó, ď, ť, ň, and German ä, ö, ü), one has to first press the corresponding modifier key (´, ˇ, ˚, ¨) like on typewriters
  • an alternative for common capital diacritics (á, é, ě, í, ú, ů, ý, ž, š, č, ř) is to briefly turn on Caps Lock (advantage over typewriters)
  • pressing the ˚ key twice prints the degree sign (°) twice (Windows) or once (Linux)
• there is a bloody dedicated § key but we need to press AltGr+7 twice, then backspace (or Alt+96) for a grave (`), which is part of ASCII and used in Markdown
• physical keyboards almost always reserve the right side of the keys for the English-US layout (very confusing for novices) so one has to type in the AltGr layer blind (except for €); it contains useful symbols ([]{}<>|\€$@#^&×÷`) as well as useless ones (Đđ – these are Slovene, why not the Slovak Ôô?), leading people to prefer Windows-only left-Alt+numpad codes (such as Alt+64 for @) that use the obsolete OEM-1252 codepage (the Unicode extension has to be enabled via registry and Alt+letters hex codes get passed to programs anyway, often defocusing the input element). I only found a Slovak one on Wikimedia Commons
• some lazy manufacturers combine the Czech/English and Slovak/English layouts, which are similar except ľ, ť and ô, leading to 5 (!) symbols per key, 3 of which are irrelevant unless you switch layouts
• Gboard for Android offers QWERTY for Czech, which looks normal (hold for diacritics, potentially swipe for ě and ů) and the unpopular QWERTZ-PC, which has all the physical keyboard's quirks, but its "Czech QWERTZ" is based off German QWERTZ, containing ú and ů but not the other diacritics for some reason. All other keyboard apps with Czech language layout get this right (hold for diacritics, potentially swipe for ě and ů)!