Mother and son Sarah and John Connor are played by actors with the same surnames (Emilia and Jason Clarke respectively), although they are not related and not of the same nationality, as Jason Clarke is an Australian and Emilia Clarke is a Brit. Speaking of which, both Jason Clarke and Jai Courtney (who plays Kyle) are Australian.
The reason there are so many Call-Back moments? "Time has momentum. Some things want to happen".
A bit of a meta example. Using CGI to de-age someone has consistently been ridiculed for looking out of place, although it's been done convincingly in a number of other movies (such as digitally de-aging Michael Douglas in Ant-Man). In this case, it's being done on an artificial humanoid, and that bit of uncanny valley fits with something that is supposed to look like a human but not quite.
Fridge Brilliance crossed with Fridge Horror. Think of the franchise as a whole, each attempt by our time travelling heroes to prevent Skynet from existing simply results in Skynet being created later and later, with more advanced terminators available to it for the war itself and to send back with each loop. The horror sets in when you realize this means each version that replaces the previous in the timeline is more and more intelligent and advanced and has more advanced tech from which to start the war from and thus is more advanced by the end. This means that if our heroes keep trying to prevent Judgement Day over and over what they will inevitably end up doing is creating a timeline where Skynet is advanced enough and smart enough that it may be able to make say T-1000s or even T-3000s practical enough to build to be regular shock troops instead of too impractical to be anything but rarities sent on the most vital missions, all controlled by a much smarter overlord, thus there would eventually be a loop where Skynet actually WINS. In short, by trying to do the right thing our "heroes" are inadvertently dooming the world.
Skynet is more like its creators than it realizes. It's overly proud, persistent, determined, and doesn't like fate. While it realizes (or believes) that it will always be created, it doesn't seem to realize that humanity will always still win. After all, yes, Judgement Day always happens but so does its defeat. Additionally, it critiques humanity for fearing and trying to destroy something they don't understand. Yet, Judgement Day starts because Skynet fears humanity and, rather than try to understand them, it would rather destroy them.
The T-5000 demonstrates a high level of intelligence, even given that it is housing Skynet. By making its move to transform Connor and eliminate all witnesses save for the required person being sent back in time, it's preventing the one flaw that would allow humanity to reverse this particular time change - foreknowledge. That is, no one will know what happened after the fact and thus no one can send someone back in time to stop it. Fortunately, someone somehow knew (in another timeline?) and put such vital informations in Pops' database.
Pops is consistently going up against and defeating superior Terminator models in this movie. Not only does this preserve the drama by pitting Pops against enemies that could probably beat him, it demonstrates the effectiveness and adaptability of the T-800 that the other models lack. Since Pops has been active for decades he has had years for his A.I. to evolve far beyond typical factory settings, allowing him the time to develop the tactical thinking, planning, and combat skills needed to effectively outthink and outfight models that could otherwise beat Pops easily, as well as compensate for the age induced malfunctions from decades of operation without maintence. This is most clearly demonstrated when he uses planning and backup to defeat his fresh off the shelf "brother" with ease.
John Connor has spent his whole life with Terminators sent by Skynet trying to kill him. Finally, in this film, A Terminator finally accomplishes the mission and kills John Connor... after he himself became one.
Again with a blend of horror. The final battle against Skynet has it go through multiple stages of "evolution." To show this, Skynet's holographic representation starts out as a child and grows into an adult. So, essentially, Skynet's entire "childhood" was defined by humans trying to kill it. No wonder it hates us so much.
The title "Genisys" was mocked before the movie came out. The stated reason for using that spelling was that they wanted to avoid infringing on the copyright of the band Genesis. That doesn't make sense; the movie's title would have been Terminator: Genesis, which is legally obviously distinct from the band. However, in-universe, Cyberdyne would not be covered by that distinction. So they really would need to change the spelling to avoid infringement.
At times during the film, Emilia Clarke's acting seemed emotionless and robotic. Thinking about it, Clarke's character Sarah Connor has been raised by an emotionless machine for eleven years, so it would make sense for her to sound robotic compared to other humans.
Skynet taking advantage of its disguise as a multiplatform social network/personal assistant software/cloud system called Genisys in 2017 makes for some really scary possiblities if it had been successful in launching itself in that guise:
It could have taken advantage of the cloud computing inherent to seed redundant instances of itself all over the Internet thanks to its billion suscribers, most likely with more than a billion such systems connected. Try to get rid of it once it's entrenched so deeply in such a decentralized fashion.
It could have taken advantage of all the location data it would be getting from countless devices to track many more humans and identify/deal with people who would might have later become key members of the human Resistance, long before they could even get organized together against it, preemptively eliminating a large portion of potential enemies before they become such.
Hell, just the description of Genisys from the first guy Kyle and Sarah talk to about it is pretty disturbing. Every electronic device you own linked to every other electronic device you own, linked to every electronic device anyone else owns? Everything you are and do constantly online? Yeah, no way THAT could possibly go wrong.
When John confronts his parents he revisits Kyle's initial speech about the Terminator from the first film; how it can't be bargained with, can't be reasoned with, and how it will. Not. Stop. As he does so you can almost see his self-awareness return, as his speech becomes a disturbing mixture of pride and self-loathing.