Apparently, people on Reddit are saying that the skill points you earn when leveling up transfer over to online play. I don't know how to feel about this.
https://www.reddit.com/r/PokkenGame/comments/4b8tbi/skill_points_do_affect_online/
Well, you can earn those points by playing online and the game also indicates how many points has every pokémon in your rooster so this isn't a surprise.
I was really worried about this. Fighting game characters shouldn't have customization unless it's in a special customized mode.
They don't, Reddit is retarded as always. You earn exp for defeating online opponents and level up, but the stats are disabled in actual battles. The only way to use stats online is in friendlies if you enable them in the options.
Apparently they're worth a minuscule amount, as in you probably do 10 more total damage at level 100. Still, as far as I know you can't use custom Pokemon in ranked.