Whoa! Six questions, here, and they cover a wide range of expertise!
Yes, counterfeit money existed in the Greek and Roman eras. Coins were reproduced in baser metals (since most, if not all of the value of the coin was the value of its gold/silver content) and coins were also altered (shaving the edges, for example, to get gold/silver from the coin) in a fraudulent manner. Not really “counterfeiting” per se, but resulting in a similar situation - a coin that isn’t really worth what you think it is.
And yes, in WWII both sides prepared enemy counterfeit currency. From this site:
"In the Second World War, all the major combatants would take part in this parodying and forging of stamps and banknotes. The Germans would parody British commemorative and definitive postage stamps and produce millions of dollars in counterfeit 5, 10, 20 and 50 pound notes under “Operation Andrew,” later called “Operation Bernhard.” The Germans also made satiric copies of British, American, Allied Military Government, Hungarian, Polish, Russian, and Yugoslav banknotes with propaganda text on the front or the back.
"The British would retaliate by counterfeiting or parodying the stamps of Germany, France, Italy, Morocco, the Netherlands, Norway, and the German-sponsored Polish General Government. They parodied the currency of Germany and German army payment certificates, and forged the money of Japanese-occupied Burma, Malaya, The Netherlands East Indies, and Thailand.
“The United States would forge or parody French fiscal stamps, Nazi Party dues stamps, and the stamps of Germany and Japan. It would also parody the currency of Burma and Japan, and counterfeit the banknotes of Japanese-occupied Burma, China, French Indochina, the Philippine Islands, and Thailand. It seems that between the years 1939 to 1945 almost all the combatants were forging each other’s stamps and banknotes.”