Where would the mint mark be for one of these coins, and what does it mean when it says some were melted down
No Mint Mark means it was minted at Philadelphia. The D and S Mint mark would be under the cabin on the Reverse.
Are you referring to the Wikipedia article passage: "Despite the large number sold, many of the coins were either melted or released into circulation." You can click on the sources at the bottom of that page for more information. The first one says "Sales were abysmal, and many coins were either released into circulation or melted." So they were melted for the silver because the coins apparently didn't sell. But this also contradicts the Wikipedia passage. Hm. Unless they mean that sales declined over time? From what I can gather they sold well in their first year but not in subsequent years, so surplus coins were melted.
"Melted" before release means just that. The mint struck them, but they never sold, so they were remelted to make new coin blanks. Some of these are probably today Franklin halves.
It means many of the coins minted were never released, so there are not as many around as you would think based upon the mintage. If a total of 1.25 million were minted, not that many survive today. However, for a commemorative, that is a MASSIVE mintage. It is one of the most common commemoratives around.
No. Very many of these were put into circulation. In fact, I think that the Booker T. Washington and Washington-Carver half dollars are the easiest "old commemorative half dollars" to acquire in all conditions and are very inexpensive. Many of the coins were released into circulation. The Booker T. Washington design was minted from 1946 to 1951. There were so many minted, and they were not particularly popular, those that the mint (Treasury Dept) did not release into circulation were simply melted down and likely reused in other coins being minted at the time.
I believe (without checking) the Booker T Washington was originally authorized for a mintage of 5 million. As mentioned sales were bad and after several years of selling (and melting) various dates and mints the remaining coins were melted, and they were made into planchets, and used to strike Washington/Carver commemorative half dollars, marketed by the same person/organization. And THOSE were then sold (poorly) for several years. with a range of different dates and mints. All told they tried to sell that authorized 5 million coins from 1946 thru 1954. And when it was all over the project it was meant to fund was in serious debt. The way these early commemorative programs worked was the sponsoring organization was able to get the coins from the government at face value. What they weren't able to sell they could send back to have their debt for the coins reduced. In the later programs they would aften send the unsold coins back and have them made into new coins for the next year and sell them again. that was the case with the Booker T Washingtons'. when sales died send them back and have a new P,D,& S set made the following year.