were there any fake copies created of that piece?
Yes, people like James A. Bolen produced copies .
1804 dollar
 James A. Bolen, a medallist and coin collector who created copies of valuable coins between 1862 and 1869, fabricated an 1804 dollar by altering the last digit in the date of a genuine 1803 example. 
which country is the 1804 dollar associated with? The United States of America. was it a coin or a note? A dollar coin. what metal was this made up of? Silver. who designed it? John Forsyth. which company minted them? The Mint of the United States. what symbols or pictures were engraved on that object? UNANSWERABLE
wiki:1987756
1804 dollar [SEP] Counterfeits and reproductions
Counterfeits and spurious reproductions of the 1804 dollar have been created since numismatists became aware of the coins' high value. James A. Bolen, a medallist and coin collector who created copies of valuable coins between 1862 and 1869, fabricated an 1804 dollar by altering the last digit in the date of a genuine 1803 example. Although Bolen added his name to the edge of the coin, other forgers created altered date coins with the intent to deceive. Nineteenth-century stage actor John T. Raymond purchased a specimen of the coin, which was later revealed to be a forgery, for $300. All silver dollars dated between 1800 and 1803 were subject to alteration to 1804 dollars, but 1801 was the date most commonly used for that purpose.