Your question about artist monograms proved to be a challenge for me and I am not convinced that I found the right answers.
1. The letters in the monogram suggest Anthony de Francisci. However, this is not the monogram found on the Peace Dollar. I could not find an illustration of a medal with this monogram.
2. This one was easy and represents John Flanagan although he used a variety of monograms on his medals.
3. This looks quite a bit like the monogram for Laura Gardin Fraser although her monogram usually has a more prominent 'L'.
4. Of course I immediately thought of Hieronymus Holzschuber but I could not find a medal in my collection with his monogram. Next I thought of Henry Herrick but his name is on the Mint Medal without a monogram. I found a reference to a Henry Hering "HH" monogram on the base of a sculpture but I have not found it on a coin or medal.
Obviously there is a need for a reference on such monograms and I look forward to buying a copy later this week.
Pete was right on the money with his answers to the first three. The four monogram belongs to Henry Hering.