As characters - yes (though currently I use only Luka and Illass, while dog and worm dig for small medals all the time), but Illass gives Luka a bit greater skills, no?
p.s. I keep Sonya in the party, but if I throw her in the castle will it still count as if she with me in the events? Or am I obligated to keep her? The same for Illass, I am kinda not into the idea that she is just an angel. Or will she get some other races later? By the way, will Luka have access to all the races? He is a Main Character, so, it would be illogical to keep him human (and he will get angel later, I am sure, but is that all?)
p.s.s. Oh my god, I just got out of Pornof and already played for 11 hours? HOW?
There's a lot to unpack here.
Skills that both Alice and Ilias give are useful, but in most cases will get outclassed by skills you learn from jobs later on or learned from other sources as well. When it comes to skill training from them, it's mostly just flavor text differences.
Weapon damage is explained by one of the guys in the Ilias Village church, one of the soldiers on the left side on the first floor, and I believe randomly a few more times throughout the game. The idea is, by using a sword skill with a sword equipped, the ability does more damage than if you attacked with anything else. I believe, but don't remember exactly, the way it's looked at is that the ability uses the damage mod listed and matching the weapon type increases it beyond that number (someone can come behind and correct me on this if it's backwards).
With this though, there's a bunch of factors to keep up with besides just damage mods. Each weapon has abilities tied to the weapon type, example being swords again: swords have a 25% chance to enter a defensive (defend) stance after using a sword skill. Each weapon type has something that makes them advantageous in certain types of builds.
Continuing with the sword example (since it provides good examples to most everything related to weapon types), the idea of weapon types effecting damage mods. Great swords and knight swords both work with swords for max damage mods, but katanas work less than any of the above while being more effective than, say, a staff. Similar types of weapons still get a bonus, but not as much as the actual match. Added on to this, there's abilities you can learn and attached to LoC gear called (weapon type) mastery. When equipped with those weapons that match the mastery, your stats increase dramatically, which obviously leads to more damage/healing when used while those are equipped.
The stats attached to the weapon usually align with the weapon attributes the skills use. All skills that deal damage/heal rely on a stat or multiple stats to deal damage/heal. Using a weapon with agility only doesn't help for skills that rely on attack, so matching that means a lot when trying to deal damage. At the same time, there's abilities in some characters' passives, races, jobs, and LoC gear that can change what certain weapon/skill types use for their damage calculations, such as Cross Heal, which makes white magic use the magic stat instead of willpower.
Passives for characters and races matter as well. Some specialize in using specific types of weapons, so your build should accommodate that as much as possible.
Tl;dr there's a lot going on in the combat math, so just make sure to match weapon types when possible and make sure to gear for the core damage stat+defenses and you're essentially set.