Early and bust half dimes never had mintmarks. For seated liberty half dimes they appear in a variety of places. Between 1838-1859 and part of 1875 it will be in the wreath below "HALF DIME" on the back(tails) of the coin. Between 1860-1869 and from 1972-1873 it will be below the wreath on the back.
The only difference is the mintmark and the fact they were made at different Mints.
The size of the mintmark. The micro S is about half the size of the regular one.
It was made at the Philadelphia Mint, 1980 was the first year a "P" mintmark was used on a half dollar.
No mint mark indicates that the dime was minted in Philadelphia.
It isn't a "JS" (and JS isn't the mintmark, the mintmark, if any would be found on the reverse) dime. It is a Roosevelt Dime, the JS are the designer's initials. It is silver, however, and worth around $2.15 in silver content.
Because the value of it is worth half the value of a dime.
A 1970 Uncirculated Mint set would not have a dime with a "S" mintmark, only a Proof set will have a dime with a "S" mintmark for that year, so no your mint set is not rare.
No rare 1941-S dimes. The 1941-S Mercury dime does have large and small mintmark varieties as do all coins (except the half dollar) that were struck in San Francisco in 1941, they have no added value.
In general no. Just because a dime has a mintmark does not make it more valuable.
The 'W' you see is the designer's monogram not a mintmark. If the coin has a mintmark it's on the reverse.
See the related question about mintmark locations.
Yes, a nickel is half a dime!