For example: Moves like swords dance, iron defense, calm mind, and so on. How much is the increase of the stats raised? And they are stackable? -- I'm asking because by the time i'm writing this, i've searched this website but on the respective pages of each move, I didn't found any information on how they work in Legends: Arceus.
Stat alterations in battle have also changed. Rather than an individual stat being raised or lowered, both offensive and defensive stats are altered. So if you use Baby-Doll Eyes, rather than just lowering the target's Attack, it lowered both Attack and Special Attack. Another difference in this is that these stat alterations will only last a few turns, and if a move sharply boosts it, it lasts longer. Using Agile or Strong variants of the moves also alters how long it lasts.
Serebii page on LA stat mechanics
(...) They boost both regular and special stats, but the difference is how long they last. Moves that boost one kind of stat (swords dance or nasty plot) last 3, 4, or 5 turns depending on whether they’re agile, regular, or strong style. Moves that boost attack and defense (calm mind or bulk up) last 2, 3, or 4 turns depending on the style. So you get an extra turn with swords dance, but you don’t get the defense boost. Based on just eyeballing some health bars and stuff, I think the boosts double the damage (or halve it for defense). They don’t seem to stack, using it again just resets the turns, but you can also use double hit which is a different status that also gives you an extra +50% damage.
Reddit thread
The main difference is that they don't last till the Pokémon faints/is switched out. They've been given a duration between three to five turns, but their effect remains the same.