Please post a new question with the coin's date and a description of the error.
Yes, there are instances of 1978 Jefferson nickels without a mint mark. This is due to a mint error where the nickel was struck without the mint mark. These error coins can sometimes be valuable to collectors.
The value of a nickel with a colored back can vary greatly depending on the color, condition, and rarity of the coin. In general, a colored nickel would typically not have a significant premium value over a regular nickel, unless it is a genuine mint error or a rare collectible.
The Denver mint did not issue any nickels in 1906, only Philadelphia did. A 1906 Philadelphia nickel retails at $3 to $25 depending on condition.
A standard 1965 quarter isn't a rare date. If it is overstruck with a nickel die, though, the value could be greater if it's a verifiable error. If the nickel image is reversed, it may or may not be an actual Mint error; if it isn't, it could've been done by anyone with a hammer after the fact, which would decrease the numismatic value (not to mention its ability to be used in a vending machine).
A nickel with copper infused is still worth 5 cents, as the metal composition of the coin is what determines its value. The added copper may change the appearance of the coin but not its monetary worth.
The coin is likely damaged, but take it to a coin dealer or collector, error coins need to be seen for an assessment.
Current retail value is $18.00-22.00 for mint state coins
It's not worth much. What you have is a novelty item, not a mint error.
This is not a Mint error coin. It has likely been altered by placing the nickel and dime in a vise and squeezing them together causing a reverse image of the dime to appear on the nickel. The coin has no numismatic collectible value.
Depending on what mint is on it, between $.35 to $1.25
5 cents
The P mint mark didn't appear on circulating US coins until 1979/1980 so your set isn't a mint error. As of 07/2015 a complete 1969 mint set retails for about $8.