Real coins have been used as the host for elongated coins. Are there any tokens that have been made from a coin rather than from a coinage blank?
Coins have been used as the host for tokens, medals, jewelry and for other coins. One well-known example of a coin struck over a token is the 1795 Liberty Cap large cents struck on Talbot, Allum and Lee tokens. The coins were poorly made, with various design elements of the underlying token often visible.
Are there other coins that have been struck over an existing U.S. coin?
The best example is likely the Draped Bust silver dollars that were overstruck to be repurposed as 1844 1-peso fuerte in Uruguay during a civil war siege in Montevideo. Siege coins are typically made from virtually anything the besieged city can find. Everything from silver plate to cardboard from books has been used in these situations.
How much value do gold-plated Washington quarters have?
Although you may be challenged to spend them, gold-plated Washington quarters are worth 25 cents. The gold plating is so miniscule, it would likely cost more to recover the metal than what would be recovered. The gold plating is applied outside the Mint by private enterprises. Remember the 1883 “racketeer” nickel was made outside the Mint as well.
Are there government mints that have issued legal tender gold-plated coins?
You need first to define what should be considered to be gold plating. Debased coinage adjusting to government or economic needs that could be argued to be gold or silver plated have existed since ancient times. The content of such coins varies from a minor debasement to a thin silver or gold wash over a base metal. Today, non-circulating legal tender commemorative coins that are gold- or silver-plated have been issued by the British Royal Mint, Perth Mint (Australia), Royal Australian Mint, Royal Canadian Mint and likely by others.
I was offered a silver American Eagle that has been painted in red, white and blue. Does this coin have any premium above its intrinsic value?
The United States has been slow to adopt color enhancement techniques to be used on coins, but the U.S. Mint has never issued a color-enhanced silver American Eagle. Considering the color was applied outside the Mint, this makes the coin simply a novelty rather than something of additional value. Be careful when purchasing such a product. You are unlikely to recoup your money when you re-sell the coin.