Why is there a 1916 Mercury Dime facing right and not left?

Answer 1

It's not a Mercury dime, it's a "Barber" dime, named for its designer Charles Barber. Both Mercury and Barber dimes were struck in 1916.

To provide some history, up till the early 20th century the Mint didn't always make design changes on calendar anniversaries. If a new design was to be issued, the old one might be struck until enough coins with the new one were available, at which time the changeover happened. For example the Lincoln cent wasn't issued until mid-1909 and up till that point Indian head cents with the same date were minted.

1916 turned out to be a transitional year. Before that time silver coins often all carried the same front design, usually a representation of Miss Liberty. Designs on all 3 or 4 denominations were changed at once - e.g. the Barber design was simultaneously adopted for dimes, quarters, and halves in 1892. By the early 20th century there was a lot of interest in enhancing coin designs, driven in part by Teddy Roosevelt's interest in numismatic art. The Mint agreed to put different designs on each denomination and competitions were held for the new coins. Barber's designs continued to be used for the first part of 1916, but later in the year dimes, quarters, and halves had all received makeovers and were struck with their new artwork.