Do we have or know of additional writings from the four Gospel Evangelists? The New Testament of the Christian Bible is commenced with four Gospels: Matthew's, Mark's, Luke's, and John's. Early church tradition has taught us that Matthew and John's Gospels were written by two of the twelve apostles bearing the name of their writings- Matthew "the tax collector"(Matt. 9:9), and John "one of the sons of Zebedee" or "the one whom Jesus loved" (Mark. 3:17). 

The authors of the Gospels of Mark and Luke do not claim to be apostles, but were indispensable with the veracity they brought towards recording the life and Christ and his followers. Early church tradition holds the author of The Gospel of Mark to be John Mark, a fellow missionary with Paul and Barnabas(Acts 12:12,25) and the one who essentially wrote Peter's account of the life of Jesus and his followers, and the Gospel of Luke to be written by Luke "the physician" (Col. 4:14) and follower of Paul. 

Do we have any other writings from these men or writings purported to be from these men outside of the New Testament? (Acts, Revelation, 1,2,3 John etc., do not count as they are included in the NT) 

The writings provided do not need to be an exhaustive list
There is Secret Mark. Its authenticity is debatable, but it purports to be the  advanced version of the Gospel of Mark.