First and foremost Red is not Elizabeth Keen's dad. We know this for a lot of reasons, he is aware of whom his wife is, and his own daughter he is looking for. He's also flat out told Keen he is not, this is important because his character design to Keen has been the flat out truth even if it's brutally painful. Many questions are now sprouting in the minds of "casual" viewers. "But the burns?" is probably the biggest one.
First lets talk about Red from what we know about him already - He is a former military man, and intelligence officer. (You can read this on his Wanted poster in Episode 1 if you pause on the poster) He also meets with one of his former squad mates who briefly talks about an incident that ruined his entire squads lives at the cost of Reds gains. Red corrects this mistake later in that episode by talking to Harold. This is a small piece of information I feel is much bigger. I'll explain it in a second.
The Blacklist is now apparently a list of coordinated people Red has linked to 1 person, he is working through the list to locate and find this 1 person. (Whom will be "No. 1" come the series finale whenever it ends) This person is apparently the bane to Reds life, and also Reds trigger for his criminal history. Why?
With the two above statements made lets get to the point...the twist. The No. 1 person on Reds Blacklist is Elizabeth Keen's father. This is brutally apparent. Going on the raw data the show has given I am going to assume Red, Keen's Father, Sam (Her Stepdad), and the Military man he talked to that Harold is to fix his records for, were all in a unit together in the Military. Red being a "real criminal" and in my opinion the shows obvious true antagonist did something that ruined the lives of many people, including Elizabeth's fathers. These events took place 20 years prior, both Red, and Keen's father disappeared the night Red went to Keen's house. The chess match starts here.
In retribution for this action (whatever it maybe later on) Elizabeth's father attacked Reds family...in the house Red blew up. In return Red did the same, burning down Elizabeth's house. Killing her mother, and thinking he killed the father. Red having lost his daughter or presumed lost his daughter couldn't bear to kill Elizabeth so he took her the night of the fire to Sam. (Who I feel might of been in on Reds military deception when he acted on it) We know this from a conversation in the car between Elizabeth and Red where Red stated "A friend brought you to Sam" not "Your father brought you to Sam". Red's burns also indicate that he was there the night Elizabeth's family was attacked. So Red rescued Keen to take her to Sam, also with Sam on Red's side he could watch over Keen.
Reds dilemma...Keen's father's corpse was never found...And thus the Blacklist starts...Red hunting for Keen's father and Keen's father trying to protect his daughter and kill Red at the same time. <Insert Tom Here> multiple obvious reasons help this as Tom has clearly stated "I work for the good guys." - "Your father is Alive." - "The man I work for is more ruthless, cunning, and lethal" <referring to Keens Father and Red>.
Tom is Keen's fathers Asset, Keen's father has been using Tom to protect and watch over his own daughter. Red knew this about Tom and has been trying to kill Tom since. You might be wondering about Berlin he's a nobody...he's No. 8 on the list which gave it away that he is neither Keen's father, nor is he important. He is a man out for revenge fed false information by Keen's father to kill Red. Nothing more, his involvement will likely be over come the Fall Season Finale.
You might be wondering why Keen's father is allowing Red to stay so close to Keen. This is the only plot point I haven't 100% figured out, but my assumption is Keen's father is cunning enough to know Red would never kill Elizabeth as he needs her for leverage to find Keen's father. So instead of coming out of the shadows he keeps tabs on Reddington by using Tom and other assests like Jolene. Keen's father also likely has a Blacklist sized list of Reddington's men/army that he has to work through himself to get to Reddington. These two men are playing Chess versus each other. Moving pawns around and taking actions when needed. Come the series finale we should have one hell of a standoff between Keen's Father and Reddinton where Keen will likely try to ask her father to spare Reddinton's life due to the fact that Reddington has done so much to help the FBI and or his caring for her makes her feel she owes him back for the times hes saved her.
There are an assortment of other small quips throughout the first season I could denote, but this is the general jist. Hope I didn't ruin the series for too many people.
TL: DR:
Red is the antagonist
Elizabeth Keen's Father is No. 1 on the Blacklist
Reds family was attacked by Keen's father after a Military dispute.
Red attacked Elizabeth's family in return, but could not kill Keen as a child.
Red saved Keen the night he tried to kill her father, took her to Sam. It is how he got his burns.
Tom works for Keen's father, entrusted asset to watch over his daughter.
Red is using the Blacklist to locate Keen's father and finish what he started.
The series finale will be Red vs Keen's Father. Keen will have to decide Red's fate. Likely will step-in to save Reddington in the end.