Hoenn introduced beauty-based evolution for Feebas and personality-value-based evolution for Wurmple's split into Silcoon or Cascoon. 135 new species brought fresh three-stage chains and branching paths. Trade evolutions now include held item requirements for Pokemon like Huntail and Gorebyss.
Max out Feebas's Beauty condition by feeding it Pokeblocks made from dry-flavored berries, then level it up. The catch: Feebas itself is absurdly rare, appearing on only 6 random tiles on Route 119 that change daily. Finding one is harder than evolving it. Use a Super Rod and be patient.
Wurmple evolves into either Silcoon or Cascoon at level 7, and which one you get depends on a hidden personality value calculated when the Wurmple is caught or hatched. It's not random each time it levels up; it's predetermined. There's no way to control it in-game. Silcoon becomes Beautifly, Cascoon becomes Dustox.
Beauty-based evolution (Feebas), personality-value branching (Wurmple), and specific held item trades (DeepSeaTooth for Huntail, DeepSeaScale for Gorebyss via Clamperl). Gen 3 also introduced abilities, which don't directly trigger evolution but changed how Pokemon function pre-evolution. The contest-stat evolution method for Feebas was unique to this generation.
Not all of them. Ruby and Sapphire famously can't connect to Gen 1/2 games. The internal dex has some older Pokemon as catchable, but others are missing entirely. You can evolve any Gen 1/2 Pokemon that's in the Hoenn dex, but Pokemon not coded into the game can't be obtained at all until FireRed/LeafGreen came out.
The Abandoned Ship has a hidden Water Stone and Thunder Stone. The Fiery Path has a Fire Stone. Leaf Stones come from various hidden item spots. You can also get random stones from the Pickup ability, so having a Zigzagoon with Pickup in your party while grinding is a solid passive farming method.