1. The power to remember past timelines is not switched between the Skelebros. Sans still has full memory of what has happened “before”, but deals with it in a far more constructive way; by trying to coach you through fights whenever he can. After you spare him in Snowdin on Pacifist Route, he will call you dozens of times along your journey to help with sparing other monsters! For instance, he might tell you that Aaron just needs a little patience, or that you should sing to Madjick.
2. On a related note, while Papyrus doesn’t have the same power, he does have the ability to use a “bubble dimension”, which is a bubble of magic that he can step into and not be affected by the flow of time. He can also bring things with him, like reminders - or Sans’ “secret” timeline log. Thus, he knows about your past crimes from Genocide Run, but doesn’t have anything to compare it to. The result is… Terrifying, to say the least. The power may not carry over, but the bitterness certainly does. The combination forms a vengeful personality with more than enough will to make Chara’s life a living hell.
3. At the game’s beginning - before any RESETs have occurred - Chara (in the protagonist role) has given up on their life, while Frisk (in the spirit role) helps them with words of encouragement. After they both leave the Ruins and Chara is feeling significantly more stable, however, Frisk’s dialogue box turns a lot more… Meme-y… Sometimes Chara will repeat Frisk’s jokes so their friends can hear them, too. Alphys and Sans think it’s hilarious. The others… Not so much.
4. By the end of the Genocide Run, though, their goals have changed; Chara is curious about what will happen at “the end”. Frisk, tired of living in this endless loop, wants to erase themself from existence. Post-Genocide Pacifist Run reveals that Chara is still fighting to keep them from… Something. Frisk won’t tell them what they plan to do, now that everyone’s still alive, but they’ve made it clear that they still have “a way out”. This is, of course, taking control via Chara’s Soul - which they were too weak to take after the first Genocide, but may be able to take after the second - and extracting their DT.
5. Alphys runs the Adventurer’s Lodge. She is the most famous member, and is looked up to as a leader, even though there are no ranks. People often call her “Duenna Alphys” as a title of respect, but most of the time, she just goes by “Allie”. Her axe has the symbol of the Lodge on both blades.
6. While undeniably brilliant, Undyne’s fitness as the Royal Scientist is often put into question by her hotheaded nature and devil-may-care attitude. She and Alphys spend hours at a time playing video games from the surface together - usually accompanied by a slew of angry cursing at the screen from both participants. The Queen finds it hilarious.
7. After banishing Asgore from the castle, Queen Toriel discarded her surname.
8. When Asgore first finds Chara in the Ruins, he plans to take their Soul and go to the surface for the rest - but he doesn’t have the resolve, nor does he actually wish to harm them. During the tutorial, he tries to ease his conscience by doting on them and acting as if everything’s alright. He only reveals the plan when they attempt to leave, until which he was hoping to spare them and simply wait for another, less loving human to fall - on Pacifist Run, anyway. On Genocide, once they reach the door he will fight them with the intent to kill, but will not have the heart to land the final blow.
9. Temmie was Asriel’s pet that he trained to fight for him. It absorbed his Soul after he died, but after Undyne’s experiments, the Soul became even more frail and lifeless than before. It cannot replicate emotions anymore, but still lends Temmie a significant power boost and the magic necessary to halt its aging. Meanwhile, Floweys are a bunch of flowers Asriel turned into playmates before Frisk fell down. They all remember the princes to a degree, but don’t have the mental capacity to actually form opinions or even full memories of back then.
10. Muffet’s spiders help out in her café. However, because they are easy to trample and the café is so famous, there is a web of lights and chandeliers hung from the ceiling. The whole apparatus cost hundreds of dollars to create, but Muffet doesn’t want to raise the prices on her food - the Spider Café is not just a rich people’s restaurant! Everyone should be able to sit down, enjoy a good meal, tell life stories, hear good music… It’s just a matter of Perserverance.