First, let me warn that his contains spoilers so do not read if you have not watched and do not want to know beforehand.
You have been warned
OK, this is what I think, based upon the story the "guard"/Berlin told the FBI in the hospital and everything that has happened previously.
Berlin told the FBI that the guy the called Berlin was in the KGB but then his DD fell in love with a dissident (I think that was the word he used). So his bosses punished him by sending him to Siberia. Then his enemies sent him a watch that had a picture of his DD (this is key), and then sent her ear and then her finger, etc.
In the last 2 scenes, Berlin was looking at the watch with a picture of his DD (it was and old pic of a young woman), and then showed Red looking at the same pic and taking off his shirt showing burn marks.
So here is my theory -- Red is Liz's biological father. But the man he is now is so far removed from the family man he was that he states that her father is dead. Long ago he fell in love with Berlin's DD and M her and took her to America and they had a child and lived happily for 4 years. Who was Red before he met Berlin's DD? I suspect a spy of some sort. So then one of Red's enemies kidnapped his wife/Berlin's DD and tried to kill him and 4 yr old Liz by setting the house on fire. Red is able to get Liz out, asks Sam to raise her, and goes hunting for the people who took his wife. And he becomes the ruthless SOB that we now see. Berlin blames Red for his DD's torture and death and has been plotting a way to take him down for 20 years. But I am not sure if he sent Tom to protect Liz (because she is his GD) and to put her in harms way (because she is Red's DD).