Here are more of those "headcanons" of mine.
Link: This guy has literally no sense of humor. He is all too serious. He rarely laughs at jokes and can easily declare some jokes as bad humor, even when they are not. Still, Link is a friendly, brave soul with a fierce fighting spirit, and has a good sense of right and wrong. He will also break up arguments from time to time.
Kirby: Unlike in Right Back At Ya, Kirby can actually speak. Kirby is fun loving and has a good nature, and is a bit childish and can get into trouble uninteltionally in some way. Still, he is good at interacting with others and likes being called cute. However, he gets angry when others try to take his food from him. Before Smash Bros 4, Kirby kept sneaking into the kitchen to eat food, sometimes getting caught. Now, Kirby is constantly fighting another hungry Smasher, Pac-Man, over the food.
Pikachu: Adorable in every way, Pikachu loves spending time outdoors, and he loves certain kinds of food. He is cuddly and usually happy, and he likes being around the female Smashers. However, those who make Pikachu mad are in for the shock of a lifetime! Out of all Smashers, Pikachu has a bond with Samus, who saved him during the events of the Subspace Emissary in Brawl.
Fox: As a Smasher, Fox kind of acts like a cop, and even loves detective action movies. He has a good sense of law and rules, and is never afraid to fight anyone, whoever the fighter may be. He does get along well with his fellow Smashers, and is good friends with his Star Fox teamate, Falco. Fox is also something of a tough guy.
King Dedede: A big, jolly, yet kinda greedy member of the Smash Bros. Group,, King Dedede always wants others to treat him like a king or of royalty. He can be seen eating or talking to Meta Knight, but most of all, he is usually seen chasing after Kirby and trying to hit him with his hammer. He will pound others with his hammer if they disrespect or insult him.
Ryu: A discliplined warrior, Ryu is only interested in battling others for the sake of improving his own abilities, and usually isolates himself from others. But he is capable of interacting with the others, and even teaches them some lessons about fighting well. He has quite a bit of respect for Little Mac and Lucario.
Cloud: A nice guy of the Smash Bros group, but with issues. He can lash out at others or even attack them if they pick on him or insult his past. He does not like talking about his nemesis, Sephrioth, but he can care for others when he wants to, and is normally not a bad sport when he loses unless he suspects someone cheated against him.
Bayonetta: The magical witch of the group, who is quite playful and teasing (in a not so harmful way) towards others. She is usually seen in the library looking up books, especially books that have to do with magic. She loves to taunt and scare Pit and Dark Pit, who usually try to avoid her and even panic when she gets too close to them.
Rosalina and Luma: The mother-children members of the group, Rosalina is very nice to others in the Smash Bros. Group, but is always looking out for her Lumas, doing things like telling them bedtime stories and such. If anyone dares to attack her Lumas outside of battle, or use them as a sports ball, Rosalina will get mad and attack them.
Inkling: The trash talker and competitive, hyperactive kid of the group, Inkling is one to taunt and say different things on how she will win against others on the field of battle. When excited for a fight, she sprays ink around the mansion, but this does get her into trouble with Master Hand, and she always ends up having to clean it all up.
Bowser: The bully of the Smash Bros. Group, he is anything but nice, and will not hesitate to pick on anyone when he feels like it. He likes to hit on Peach, who slaps him on the nose every time, which somehow causes him to cry. He also like throwing Bomb-ombs at Mario given the chance, and mostly gets owned after he bullies someone. He also beats up those who pick on his son, Bowser Jr.
Ganondorf: The king of evil, Ganondorf is cruel and malicious, though to his chagrin, the others are not afraid of him. Ganondorf does not like to be questioned, and will attack those who do so. He is very mean, and is usually seen practicing some dark religion. He also usually goes after Sonic after he calls him "Ganondork".
Bowser Jr.: The spoiled kid of the Smash Bros. Group, he is used to getting his way. He enjoys pulling pranks on others just for the fun of it, especially the Mario Brothers and Yoshi. He sometimes spends time with his father, Bowser, who will spoil him and defend him from others who dare try to pick on him. He enjoys doing bad over doing good.