The cleaning of any coin is not a good idea, but it also depends on why you think the coin needs to be cleaned, so take it to a dealer or collector and ask for an opinion
$2.00-$4.00 in average condition
Uh, the lady is Miss Liberty, as in "Statue of ..." Please see the Related Question for more.
It's a Roosevelt dime not a liberty dime and all are considered common, value is about $2.00
A 1926 Mercury dime is common, average value is $3.00-$6.00 depending on the condition of the coin.
The Winged Liberty, or Mercury Dime. Most people call it the Mercury Dime, but its real name is the Winged Liberty dime.
It isn't a liberty dime, it is a Roosevelt dime, it isn't silver and only worth 10 cents.
The Liberty dime minted in 1943 was 90% silver. The current rate for a circulated 1943 Liberty Dime is the current value of the silver of the coin, presently $5.50
You can find a picture of a 1936 liberty dime at the related link below.
A US dime dated 1867 is a Seated Liberty dime. To see one, in your search box type in Seated Liberty dime and click on images.
That's off by about 65 years. Mercury dimes were minted from 1916 to 1945. A dime from 1853 would be called a Liberty dime or Liberty Seated dime.
The Liberty Seated Dime (1837-1891)
The value of a 1842 seated liberty dime is about $20 in G-4(good) condition.