First of all, let me start off with this: time travel is theoretically possible. There is no absolute law of physics that prevents it. However, there are numerous problems and pitfalls.
To begin with, most current theories deal only with sending information. Some think that physical travel is impossible others think it is too complex and dangerous at this point. Sending information would alter the world in the way depicted in the series, depending on the actions taken with based on it. This is why it has been proposed that travel to the past may be impossible (but not the future). Some believe that the universe has a self correction method because the ramifications of altering the past are dire to say the least.
Lets start with the "world lines" mentioned in the series. This is an expression of the many worlds theory based on quantum mechanics. In it's most distilled form, this theory says that every decision at every level creates a new universe for each possible outcome. Think about it this way:
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You have situation 1 in front of you. Based on your actions, you can have outcomes A, B, C, or D with varying probabilities. This would yield world A', B', C', and D' (apostrophe here is "prime" and means 'resulting from', hence world A' results from outcome A of situation 1). This results in four worlds or perhaps more when you account for the different probabilities such that if D is twice as likely as A, then two D' universes would be formed for every A' universe. Now, we similarly encounter a second situation. This results in more outcomes and universes in the same manner as situation 1.
This is what is known as divergence or, as it is referenced in the series, divergence number. And divergence only increases as causality moves forward (Causality: action X causes result X and in that order. I am using causality here because causality is incontrovertible where as time is a construct to describe the world. In addition, it makes more sense because it is actions and results that cause divergence, not 'time'.) As you can see, if you take all of the choices, no matter how insignificant, into account, the number of universes or worlds quickly approaches infinity. Now, what the show is saying by "moving world lines" is that by sending information into the past, we can affect the outcome of a situation in the past and therefore any and all universes spawned from that point. This alters the number of possible outcomes and therefore the divergence. Lets go back to out example:
We again encounter situation 1 with outcomes A, B, C, and D. But we have sent information in the past to tell ourselves that A is the outcome we want. Therefore A now has the highest probability and will form the basis for most if not all universes from that point on. This reduces the divergence by narrowing the number of possible universes by as much as 3/4 and, shifting and deleting all universes that do not conform to that constraint. Furthermore, only one universe has to send information back to affect all of the others. You could have millions of spawned universes and if one sends information back, all of the millions of spawned universes are "shifted" to conform.
In addition, what the show says about memory alteration is most likely true. Since memories are caused by experiences; if those experiences are altered then so are the memories. Now as to answer the question of why the protagonist retains his memories. He is the "traveler". He (or his information) is the one actually moving. It is like being at the center of a storm. You can see all of the rain and wind but, you are not affected by it.
Back to time travel in general. As you can see, this 'many worlds theory' becomes quite messy, quite quickly. So messy in fact, most physicists dismiss it as nonsense. The predominate theory of quantum mechanics is one based on probabilities and the fact that things at the sub-atomic level are not truly physical objects. That would require an entire text book to explain (I know, I have two!) but the take away is that the many worlds theory is pretty much thought of as 'junk science'. As one of my professors put it: if many worlds exist, then you shouldn't be afraid to get shot because even if the you in this world dies, there is at least one you in a world that didn't.
On to black holes. A Kerr black hole is a rotating ultra dense unit of matter. It is so dense that in fact it has collapsed in on itself and the resulting gravity does not let even light escape. There are other types of black holes as well but they are essentially all massive gravity wells. To give you a picture of the density, take the entire Earth as it is now and collapse it down to the size of the tip of a ball point pen. That is a black hole. Black holes, or singularities as they are properly known, have been long associated with time travel in both science and popular culture. Einstein, who proposed the existence of singularities but dismissed them as nonsense because of the "messiness" of them, even suggested a possible link with time travel (But that is impossible because black holes don't exist, right? Wrong.) Essentially singularities bend space and time to beyond the breaking point and scientists have no idea what happens there. There are a few theories but none are proven or have gained experimental traction yet. So, do black holes exist? Yes. Can they be used for time travel? Maybe, perhaps probably.
On one note, the characters use of a black hole to compress data is likely nonsense. In the standard four dimensions (three directions and time) black holes are information sinks. Anything that goes in doesn't come out and therefore can not be compressed. This does not hold true in higher dimensions necessarily but, that is irrelevant because only the four dimensions are useful to humans directly.
For completeness, let me say that the basic information on the Large Hadron Collider is mostly correct. It was built mainly for one purpose; to find the Higgs boson, theoretically the basis of matter having mass. Wikipedia has a good article on the LHC and the Higgs so I will that there. And yes CERN is real. And yes, the translators made a mistake. It is CERN, not SERN. It is Europe's main laboratory for research of all kinds but it is most famous for it's nuclear physics research.
I am going to leave this post here. I could say a lot more but I think this more than enough to bend almost anyone's brain. I will be monitoring this thread for the foreseeable future so, post any questions you have and I will post back as soon as I can. Hope this helps for anyone that was curious.
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Time Travel Explanation 
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