Elio's team composition says three specific things about him:

Elio has a subconsciously acute case of OCD via color coordination; he has a Pokemon of every color and type, and when each member is organized in a certain fashion, they parallel the colors of a rainbow. He has all his bases covered as a fashionista, and as both a veteran Top Coordinator and a multi-regional Champion-level battler.

He's capable of accepting Pokemon that have been shunned by society in one aspect or another and capable of bringing out their respective talents in lieu of their numerous differences and similarities - stating that even those who were rejected have something to offer and that no one is useless or a monster. Such openness and proper coordination not only exhibit his high degree of magnanimity, empathy, and creativity but highlights his status as both a genius and a charismatic intellectual - turning something that's originally perceived as a volatile bane into an awe-inspiring boon that drastically changes public opinion. This extends to individuals as well, capable of practically tolerating and working with basically anyone in lieu of temperaments, abilities, or origins - synchronizing with them to bring out the utmost results for whatever tasks lie ahead.

While not really team composition-related, Elio keeps all his Pokemon on him via modifying his Pokeballs. This shows that he not only values freedom - viewing the PC system as a type of prison, but he'd rather have everyone together: viewing them as an extended family while also exemplifying his inclusive nature. He wants all of his Pokemon to enjoy this long adventure with him, otherwise, it's not worth it.

(There's more symbolism to his team, but I'm too lazy to properly write it out. Sorry ¯_(ツ)_/¯ )

I had to think about this a little but I'd say that Houndoom is a prime example for this.

Despite her ace Pokémon being Talonflame, Houndoom was actually her very first Pokémon that she got when she was a teenager. They've been together for a long time, and he was the only one who witnessed Briar's situation at home so he was always naturally protective of her. In Team Flare too, since when you're part of an organization like that, you need the extra security at all times.

But the real sense of protection came after Team Flare was disbanded and Briar fell into a deep depression. Houndoom, who had been there since the beginning, promised to never let Briar go that low ever again.

They've been together for years, decades even, so their bond is quite strong, and this is exemplified by the fact that it is Briar's only Pokémon capable of Mega Evolving, which happens when you have a strong bond with your trainer. Houndoom's desire to protect Briar is so strong that he would gladly go through something as painful as Mega Evolution if it gave him the means to keep her safe. And he is the only Pokémon that she has that can do something like that—go that far, for her. This doesn't mean that her other Pokémon don't care—they do, they love her a lot—, but none of them have been there since the beginning like Houndoom.

Not too much really, since Estella rotates party members pretty often.

I'd mostly say her team choices often indicate a preference for battle prowess. She doesn't really keep any unevolved Pokemon around nor does she show much interest in catching "weak" Pokemon. If Estella's catching an Eevee, that Eevee needs to have an interest in evolving and battling, or she'd release it back into the wild.

She caught a Wimpod because she knew it'd evolve into Golisopod. While she did treat Ares quite well as a Wimpod, she probably would have passed on him if she didn't know about his evolution, and she would have released him if he'd had no desire to grow stronger.