They have been selling the state quarter dies, but only after they have ground off the design, so you have to trust them when they tell you which quarter it struck.
They never have. If your coin has a hole and is a US coin then someone drilled it in. It was not done at a US mint.
This was not done by the U.S. Mint. Why it was done? Just the person that had it done knows.
There are a few explanations (if this truly is a mint error) The first and most valuable would be a quarter struck on a nickel blank, such a coin would be worth quite a bit of money. The second most valuable would be a coin that was a clipped planchet (blank) such a coin has a cut on it, but as this can be done after minting so it is best to see a coin dealer about this. But, it is always possible this wasn't done at the mint, but was done afterwards. So you need to see a reputable coin dealer to get it evaluated in person.
The US Mint does not wrap coins. All coin wrapping is done by third party companies.
No 'Star' mintmarks exist, if the coin has one, it has been added after it was struck and was NOT done by any U.S. Mint.
It isn't gold, it is gold plated. It is worth 25 cents. It is a damaged coin from a collector's perspective. It was not done at the mint.
US mint sets 1958 and before are double sets so a 1957 will have 2 of each coin with a face value of $3.64. This was done so both sides of each coin from each mint could be displayed in the cardboard holders that came with the set.
It's a novelty coin and it was not done at the mint and has no collectible value at all
It's a common novelty coin, not worth very much. A 1973 penny is currently worth about 2 cents for its copper content, and one with Kennedy carved into is worth as much as someone on eBay will pay for it.
It was done outside of the Mint. The good news is that the coin was only worth 50¢ before it was damaged so you haven't lost anything.
The US mint did not make this coin, it was done outside of the mint an is gold plated or copper plate, but it still has value for the silver under the plating. It's worth about a dollar.
The copper plating was not done by the U.S. Mint so the coin is just face value. NOTE: No U.S. Mint plates any coins with copper, gold or silver.