It's not clear what you mean. Are you referring to a coin in mint condition, or the facility where coins are manufactured? Please post a new question with more details.
No US coin bears an "F" mint mark
Mintmarks identify which mint the coin was made at.
A mint condition coin is a coin that is in pristine condition, as if it has just been produced at the mint. It will have no signs of wear, scratches, or damage, and the details on the coin will be sharp and well-defined. Mint condition coins are highly valued by collectors due to their rarity and quality.
The letter is known as the mint-mark and tells where the coin was made. A coin having a P mint-mark (or no mint-mark on some coins) was made in Philadelphia, a coin having an S Mint-mark was minted in San Fransisco, a coin with a D mint-mark was minted in Denver.
No. However, there is a George Washington mint coin.
If there isn't a mint mark on a US coin, usually it means that such a coin was minted in Philadelphia.
Mint condition, Mint State, & Uncirculated all mean the same thing. Unused, no wear, as in the same condition as from the Mint when the coin was struck.
A Denver mint coin is a coin that was produced at the United States Mint facility located in Denver, Colorado. Coins minted at this location typically have a "D" mintmark to indicate their origin.
Harriet Tubman has never been on a US Mint Coin.
The mint mark of the Denver Mint (shown as a "D") and the San Francisco Mint (shown as "S) on the Eisenhower Dollar is located on the obverse (heads) side of the coin directly beneath the bust of Eisenhower. If there is no mint mark there, then the coin was struck at the Philadelphia Mint and in this mint did not place a mint mark on the coins struck there until 1979.
You are probably thinking of an "error coin". This coin is any coin which does not meet the standards of the US Mint or has a flaw in its design or manufacture.
The mint mark is located on the reverse [tails] side of the coin at the bottom below the wreath. If there is no mint mark then the coin was minted at the Philadelphia Mint.