Hmmm, I am not sure on that, I did check the cherry pickers guide and did not see it there. I would suggest http://conecaonline.org/ as they have a huge database of error coins. There is a 1957D listed. Check it out.
Very hard to say, I do not want to mislead you. Other members on here will be able to tell you with the pictures you have posted. For me, I can not see it, but that does not mean it is not there. Eyes are not as good as they once were...lol Can you magnify it more? I know that is not easy, and sometimes with magnification you do not see it either...just a suggestion.
There does appear tpo be something on the first picture, I can almost make out the tail of an "s" in the bottom left side of the D. Again I will wait and watch for a more experienced eye to look. I have checked every reference I can think of and know of, and nothing is coming up about a 1957 d/s nickel. I would see if anyone a PCGS is willing to take a look. I believe some of our members might know who to ask.
I do not think so. The image of an underlying "S" doesn't seem to fit well and distinct as to shape. Also, I have not seen a D/S on a coin where part of the diagonal of the "S" was not visible to some extent through the center of the "D".