First of all, these go in no particular order, and if you haven't seen Episode 7 yet, many, many SPOILERS ahead. I'm basing them off of what I have seen in Star Wars 7, and what I think makes sense.
1. Who Are the Knights' of Ren?
What we know: Again, SPOILERS!!! In Episode 7, we learn that Luke went away to train others in the ways of the force, essentially, creating a new Jedi Academy. Likewise, we know one of them "destroyed everything," by turning to the dark side. We clearly know that this person is Kylo Ren, AKA Ben Solo, son of Han Solo & Leia Organa.
Theory: The Knights of Ren were once padawans of Luke Skywalker, and were seduced to the dark side by their friend Ben Solo, along with Supreme Leader Snoke.
Why this Works: First and foremost, we know that Luke was training multiple students, as they state a student, not his only student, and knowing that, we can logically conclude that the odds Luke goes into hiding because one student turns corrupt is unlikely. If Luke had multiple students, he would have completed their training, unless they were all corrupted. Therefore, they are all ex-students of Luke, making them extremely dangerous.
In this early concept art of the Knights of Ren, we see that each of them have a tube like object which appear to be Lightsabers.
2. Who is Rey?
What we know: Not much is known as to the true identity of Rey, we know that she is extremely force sensitive, and that she is very familiar with a lightsaber. Likewise, she's a very skilled pilot.
Theory A: Rey was one of Luke's students, however when a group of them became corrupt, she, the lone survivor, was sent to Jaku and her memory was altered to protect her from knowing her true identity.
Theory B: Rey is the daughter of Luke Skywalker.
Why Both Theories Work: There's is lot's of proof throughout this film to back these up. First, Rey stays on Jaku, and as we've seen, she is a very intelligent young women, therefore, she should have left Jaku by now. Yet something seems to be holding her back, and that's because Luke has altered her memory and convinced her that under no circumstance should she leave Jaku. Second, comes from the scene where Kylo is removing memories from Rey's mind. He states that he see an island, and who do we know that has been hiding at an island? Luke Skywalker. This further proves that Luke, or someone, has tampered with her memories. In addition, we see throughout it that Rey is deeply in tune with the force, and this bothered many fans. How could she pick up on using the force so quickly, when it took Luke 3 movies to master it? Because she's already knows how to use the force, and that memory was just removed.
Further Proof: Lastly, there's a scene, this one to be exact:
After one of the best Sith rage sessions of all time, the man states that there was also a girl with them, to which Ren replies, "What girl?" This, above all else, proves that he knows Rey, because she was the only student he couldn't corrupt, or the only one who escaped the slaughter.
3. Who is Finn?
What we know: First, we know that Finn was a Stormtrooper, and that he has served them for the majority of his life.
Theory: Brace yourself, because this one is pretty out there, I fully expect to be blasted in the comment section for this one... Finn, while not technically a member of the Resistance, he is a spy for Luke Skywalker.
Proof: First of all, the reason for Finn leaving the resistance is fairly weak, yes, he witnessed his friend's death, however that shouldn't have pushed him over the edge. Instead, I believe that Finn has been in contact with Luke the entire time, and he has infiltrated the base to keep the now hidden Luke up to date on what Kylo Ren is doing. The proof here is in Finn's actions. He just stumbles upon Poe Dameron? Doubtful, I think he knew the entire time what the significance of the intel was, and that Luke contacted Finn, telling him that he needed to rescue Poe. Likewise, Finn's goal throughout the movie was clear: to keep Rey safe. Why? Because Luke had sent him to ensure that she, and the intel safely reach the resistance. This is the only reason I can see Finn being in the film at all, think about it: he's not our new Luke, as he doesn't have the force (Rey), he's not our new scoundrel (obviously Poe Dameron), so he must be some sort of a spy. Lastly, R2 activates shortly after Finn arrives, why? Because Luke has taught Finn what needs to be done to reactivate him.