Akise's actions in Mirai Nikki: Paradox gains new context when you take into account that he is an Artificial Human created specifically to observe and record the game for Deus.
A lot of Yuno's early behavior can be explained by the knowledge that she has been through the Survival Game once before and could know in advance what is supposed to happen. Even though it's explained that a lot of her memories of the first world were sealed beforehand, she can still have flashes of what occurred that would give her an edge over the other competitors, as well as being emotionally affected by what happened in the previous world. Examples include:
Way back in Chapter 1, when Yuno knows that Yuki might stab her with the dart, she seems totally indifferent about that, pins him against a wall, kisses him, and says "You didn't stab me.", as if she knew ahead of time he wouldn't, even though her Diary wouldn't be reliable against Yuki in a fight against him.
"How can she talk about killing someone so easily?" It's not exactly like she's new to it; notably, 2nd-world Yuno and 3rd-world Yuno, who never participated in the Survival Game, are not nearly as psychotic as 1st-world Yuno, suggesting she is Conditioned to Accept Horror after the emotional scars of intentionally committing murder again and again, killing Yuki, and even killing her own alternate self, even if she doesn't have the actual memories of those acts.
Yuno suddenly deciding to meditate in Yukiteru's house to find Fifth's diary? She wasn't just trying to put herself in his shoes, she could have been trying to make herself remember where she found it before.
Yuno's surprise at Yukiteru's friends betraying him in Minene's attack on the school? She might have been instinctively inclined to trust Yukiteru's friends if, in the 1st-world, they actually decided to protect Yuki not to sacrifice him.
Her immediate suspicion of Tsubaki's motives? They had been betrayed before.
Why did Mur Mur get hit by Akise's bike, steal the bike's seat, and ask to be taken to a amusement park? Because having already gone through the events of Paradox she knows that Akise is a threat to her and Yuno's goals. So she decides to stall him as much as possible.
The end of the first opening, and several bits of the second, feature Yuno going Ax-Crazy with what appears to be another Yuno and then fusing with her. While at first glance this may look like your typical random Anime opening moment, it becomes a great form of foreshadowing when you consider future revelations about Yuno.
This might be a little coincidental, but the first opening and ending themes perfectly capture the essence of a yandere (especially considering that one of the main characters is the defining example) with the opening being crazy, hectic, creepy and psychotic, representing the "yan" part, while the ending is more calm, representing the "dere" part.
Yuno's memory edits. Let's look at it from her perspective. She just traveled back in time and killed her other self, to prevent Yukki from dying in the end, and to finally "come together" with him. The key is, the first time, things actually went mostly right. She and Yukki were the last survivors, and they cared about each other, but they screwed up in the end and they apparently didn't get as close as Yuno wanted. So she would want to not remember things that would change this. But she had to remember the gist of why and how she came, and she had to remember her love for Yukki to further it. So she keeps those things, and because she keeps those, she risks causing some changes, and so she gives herself some other memories to keep an advantage in the game: seemingly the knowledge that they would end up fighting Fourth, Fifth, and Sixth, as well as perhaps some fighting skills. The result? Someone who knows things, particularly that she loves Yukki and needs to protect and come together with him, but yet she doesn't have a complete idea of why she knows them. In other words, as deranged a Yandere as she turns out in the time since.
He's also a massive loner and probably so starved for company and friendship that he's willing to forgive people for things that almost nobody else would be willing to.
Why did Twelfth seem to cling to Sentai tropes when pursuing justice given his Blindness? If Yuki's rationalization of Deus as an imaginary friend has any bearing, many Sentai series have a Mystical head honcho (Deus) with a plucky comic relief henchman (Murmur) that can summon their ward (Twelfth).
Even without knowing the real color of his eyeball mask, a basic knowledge of super sentai tropes would have been enough to give away who the Twelfth was. Twelfth's biggest desire was to be a hero, and the best hero at that. In most all sentai type media, the biggest hero of them all, and the leader of the squad, is typically the red hero. And since he desires to be the biggest hero of them all, the only viable choice for him would have been to be the red.
Yuno's Clingy Jealous Girl antics concerning Akise, Hinata and the others. Yuno is adamant on Yuki "not needing any friends other than herself" and preemptively attempts to alienate Yuki from the group. It's easy to chalk this up to just another example of her being a Yandere but it's also worth remembering that Yuno was not initially like this at the start of the series. When Minene was bombing their school, it was Yuno who urged Yuki to seek out his classmates for help and they betrayed him and attempted to hand him over to Minene. It was from that point that Yuno considered literally everyone, Diary-holder or not, a potential threat to Yuki.
Doubles as fridge sadness, but in one of the omakes Mur Mur is running a call in radio advice show, the call featured in the short being Yunos mother Saika, audibly hysterical about her husbands long hours at work. In between Mur Murs less then stellar advice, we get a rather in depth look into Mrs. Gasais mind and her abusive behavior towards Yuno is explained as Follows:
1. The Gasais wanted children, but Saika was for whatever reason unable to conceive, so they adopted Yuno.
2. Ushios busy work schedule, or simply him being a workaholic, lead to him spending less and less time at home with his family.
3. Saika, possibility already suffering from mental problems, convinces herself that Ushio is cheating on her and/or is going to leave her.
4. Saika takes it out on Yuno.
Second opening for the series shows most of the cast in blue colour. The only ones not coloured blue are Minene, Yuki and Yuno. In other words, the only characters who don't die during the game.
All of the Diary Holders' names are based off of gods, specifically those of the Roman Pantheon, and those names often indicate key aspects of them or their eventual fates
Yukiteru Amano, the 1st, is named after Jupiter, the head god of the Roman Pantheon. Hinting at his eventual rise to power as the god of Time and Space of his universe. Along with this, Jupiter is the Roman counterpart to the Greek god Zeus, alluding to Yukiteru's connection with the former god Deus.
Yuno Gasai, the 2nd, comes from Juno, the insanely jealous wife of Jupiter, much like Yuno is obsessed with keeping Yukiteru all to herself. Juno was also an incredibly warlike goddess who reveled in combat, much as Yuno is adept in all her fights in the second universe.
Takao Hiyama, the 3rd, is associated with Vulcan, Roman god of volcanoes. Vulcan is heavily associated with metalworking for tools and weapons (like Hiyama's trademark machete he uses for killing), but many of Vulcan's celebrations were also along the lines of encouraging him to avert his deadly fires away from people, like Hiyama had murderous tendencies before and during the game.
Keigo Kurusu, the 4th, is named for Mercury, a Roman god who was associated with messages, delivery, trickery, and thieves. Kurusu's goal in life was to deliver justice to the world, usually by stopping thieves.
Reisuke Houjo, the 5th, is named for Ceres, a Roman goddess of agriculture and motherhood. Though disliking his parents and having to learn to be self sufficient very early on, Reisuke's main reason to get involved when he joined the game was to get revenge on those who had murdered his mother and father, as he still seeks the ideal parental relationship. Additionally, when staging his attack on the Amano household, he spared Yukiteru's mother on the grounds that she had been so kind to him.
Tsubaki Kasugano, the 6th, is named for Proserpina, Roman goddess of springtime and flowers. Tsubaki was considered the figurehead of her cult, and being imprisoned in the compound much as her goddess namesake was imprisoned in the underworld. However, one famous moment in Prosperina's mythos was named as the 'Rape of Prosperina', for the time when she was dragged into the underworld by its god, much as Tsubaki's position as the cult's sexual outlet by rape led to her current position after her parents died.
Marco Ikusaba and Ai Mikami, together the 7th, are named for Mars and Venus, the Roman gods of war and love respectively. In Roman mythology, Mars and Venus were lovers, and in some interpretations were even considered married. Much as Ai and Marco desire to be together by winning the game.
Kamado Ueshita, the 8th, is named for Vesta, Roman goddess of hearth, home, and family. Ueshita runs an orphanage which houses many young and abandoned children. Either looking to adopt them out to good families or making them a part of her own family.
Minene Uryuu, the 9th, is named for Minerva, Roman goddess of wisdom and strategic warfare. Minene, having lost her parents to a terrorist attack when she was young to a religious war, turned her back on god and became a terrorist. Being not especially physically strong, most of her attacks rely on traps she set in advance and luring her foes into favorable positions for her, making her largely a strategic fighter. Also, as Minerva is considered one of the three major gods in the Roman pantheon, Minene also goes on to survive the 2nd world's game and continues to live in the 3rd world with some minor godly powers.
Karyuudo Tsukishima, the true 10th, is named for Diana, Roman goddess of wild animals and hunting. Much as his diary allows for the control of his beloved dogs. In addition, Diana is considered the counterpart of the Greek goddess, Artemis, which is fitting in that his daughter, Hinata, is named for the Greek god of prophecy, Apollo. Hinata is the one who actually uses his diary in a confrontation with Yukiteru and Yuno, meaning she is the one who actively uses the ability to see the future.
John Bacchus, the 11th, is named for the Roman god of wine, Bacchus. He is also known as the god of epiphany, and is often considered a 'foreign' god among the pantheon. It was with Bacchus's help that Deus began planning and developing the utilization of cell phones and future diaries for the game, and Bacchus is very much an outsider to the rest of the diary holders due to his special position as a helper of Deus in making the game.
Yomotsu Hirasaka, the 12th, is named for the Roman god of death, Pluto. Unlike Hades, who was seen as the violent abductor of goddess Persephone and a fearsome ruler of the underworld, Pluto was often worshipped by many and was generally considered a kind and just god. Much as Hirasaka sought to be a hero like he had heard on television, along with the fact that many heroic quests in mythology have taken place in the underworld.
Other characters in Future Diary are associated with mythology as well, in keeping with the theme.
Yukiteru's mother, Rea Amano, is named for Rhea, a Greek Titan, wife to Cronus and mother to Zeus, the Greek equivalent of Jupiter, who Yukiteru was named for. Rhea is often known as the "mother of gods", and Rea's own son, Yukiteru, became god of the universe. In addition, Rhea is known as a goddess of motherhood, and Rea is mother of the series' main character.
Yukiteru's father, Kurou Amano, is named for Cronus, a Greek Titan, husband to Rhea and father of Zeus, the Greek equivalent of Jupiter, who Yukiteru was named for. In Greek mythology, Cronus, fearing his godly children would one day overpower him, he devoured them to prevent this. Much as Kurou betrayed his own son for his own benefit. Ironically, Cronus's Roman equivalent, Saturn, was considered a god of wealth and plenty, though one of the main reasons cited for Rea divorcing Kurou was that he was terrible with handling money, leaving him and his family large debts.
In the end of the manga, Yuno syncs her memories with the 3rd world Yuno to reunite with Yukiteru. 3rd world Yuno was sane, had lots of friends and actually had a functioning and healthy relationship with her parents. While 3rd world Yuno is still way better off than 1st world Yuno, she's still going to have to deal with the horrible memories of her abused, homicidal, later nigh-omnicidal, self-loathing 1st world self.
Given that gods in this series are shown to be able to edit the memories of themselves or others (with Yuno as a good example), take into consideration just how Deus became Yuki's "Imaginary" Friend. In other words, he quite literally entered Yukiteru's mind and manipulated his memory so Yuki would remember himself as thinking Deus up. And the manner of howhorrific that might have been in practice only adds to it.