Why did Sans give the underground locations the same names Asgore did in canon? Because he's too lazy to come up with anything other than the most obvious ones.
Warning! Plenty of spoilers for the canon universe, which are uncovered because it would need to cover all the entry! Admitting that Chara shares the same backstory as their canon counterpart, which is implied, the reason why in Shift 1 they didn't try the plan they enacted in the canon universe may find a more complex answer than simply "because Chara switched place with Sans". Indeed, in Shift 1, and contrary to the situation in the game, Chara doesn't have an easy access to the Barrier, as their parents aren't the royal family in this universe. Moreover, in order to reach the Barrier, Chara would have to pass King Sans. Given the fact that the last time they met, Sans nearly took Chara's soul even though he seems as hesitant to do it as canon!Asgore (and they were only saved by the intervention of Toriel), we can safely assume that Chara doesn't dare to come close to the castle anymore. As a consequence, they were unable to put in motion any plan that would require to cross the Barrier. Over time, thanks to the influence of their family, Chara managed to let go of their hatred (at least enough to not kill a human on sight).
Another proof would be that, in the ending where Chara both has the possibility note as Asriel has become the King of the Underground and the motivationnote as you caused the deaths of Toriel and Asgore, their parents to cross the Barrier, Asriel's phonecall has him noting that Chara is amassing a big quantity of buttercups... Which implies that they will try to enact the same plan as in the canon timeline. Therefore, when they have the possibility and the motivation (which they don't have in Shift 1 except in this ending), Chara tries to enact the same plan as in the canon timeline.
Chara's Berserk Button of accusing people who have suffered as being evil is pretty interesting, but nothing to note... until you realize they're also talking about themselves. Chara clearly possesses some self-loathing for being human and it is implied that they grew up in a rough area, thus their disdain for humanity. They think humanity is evil, yet they're human and hate themselves for it. They want to believe that because they have suffered at their hands... the same way monsterkind suffered from humanity, that they are not evil. To them, they suffered and they don't mean to do the bad things.
The Dreemurr family (plus Chara) fill the roles of Undyne, Alphys, and the Skelebros. Remember what happens to those characters in the Neutral and Genocide Routes?
While in Undertale it's only implied that Alphys was suicidal and killed herself in the neutral endings where Mettaton is killed, and at least one ending where Undyne is killed, here it's outright stated that Alphys!Asgore is suicidal, meaning that the possibility of him killing himself if Toriel, Asriel, or both are killed is much more likely. So this time you KNOW you're responsible for his death.
The Neutral Ending where Papyrus!Asriel becomes king. Sans!Chara is planning to do the same thing they did in the canon timeline, only with a lot more buttercups this time. And thanks to you killing their parents and friends, Asriel will be more willing to kill humans due to seeing first hand how they can be unlike his canon counterpart.
Any Neutral endings where Toriel and Asgore are both dead will most likely result in Asriel being stuck as a child until he dies due to being an orphaned boss monster.
Considering that a being with both a monster and a human soul can easily cross the barrier, the combined form of Chara and Asriel will be able to hunt you down at their leisure. Sleep tight.
You meet Sans!Chara in the Hall of Judgment. Chara calmly states that they can see all the lines of data that make up the game before judging you based on your EXP and LOVE. At the moment it's Heartwarming as they look so happy and So Proud of You, but when you step away from the desk and think about the WHY of the matter, you get a dawning horrifying realization that they spent the whole time fearfully watching those numbers. Praying that they will never rise, or if they do it's not one off their family. And even if you do you're just a RESET away from getting away with it, and no one will ever know.
When Toriel first saw Chara, they were "barely alive". At first, it seems like that was Sans's doing. But later on, Chara says Sans caught them mid-fall and was gently setting them down. So... what happened to them that their injuries were so grievous?