No $2.50 dollar gold coins were struck dated 1813. Look at the coin again an post new question
Please check your coin again. Large cents were still being made in 1851. The first Flying Eagle cents were dated 1856.
This a well-known fake dated 1851. The piece has no collectible value.
All of them are upside down. Most coins are struck with the obverse and the reverse at 180 degrees from each other.
A 1914 double eagle in circulated condition has retail values of $1,420.00-$1,890.00 depending on the grade of the coin
The first Indian Head Half Eagle ($5) gold piece was struck in 1908. A coin of this kind dated 1880 would be a Liberty Head gold coin. Please check the coin again and post new question. Also look on the back of the coin for any mintmarks.
There are several US coins featuring an American Indian on the obverse ("heads"). They include the Buffalo Nickel (features a buffalo on the reverse), the Indian Head Penny (has a wreath and "one cent" on reverse), the Sacajawea one dollar coin (first minted in 2000) and many gold coins (they are historic coins, all are dated before the 1940s and made out of 90% pure gold) including the half-eagle, three-dollar piece, quarter-eagle, gold dollar, and eagle gold coins. Without knowing which "Indian head" coin you are referring to, let alone the date, mint-mark and condition it is impossible to say what it is worth.
You have some sort of medal or other item but not a coin. Please post a new question with more information about the inscriptions that might help ID your item.
All U.S. coins have the reverse upside down from the obverse (front) of the coins. Just look at any other coins you have. It has no added value unless it's dated 1964 or 1965-1970.
Concerning the 1910 $10 gold piece: Actually there is no Indian on the coin. The image on the obverse [heads] side of the coin is really Lady Liberty wearing an Indian war bonnet. She is facing left on this coin. The eagle on the reverse [tails] side of the coin is also facing left.
If it has one its on the reverse between the rim and the tips of the arrow heads the eagle is standing on. It is small.
Hard to tell without a picture. Try ValueJockey.com it is free. you can post a picture there and get pricing help. Good Luck!!!
I will need more information on what ten dollar gold coin you possess: the US mint has produced the following ten dollar gold coins: * Capped Bust, Heraldic Eagle * Coronet Head eagle * Indian Head * American Eagle bullion