Celia's Stupid Romhack is built around working things out for yourself - what a Pokémon has become, what a move really does, which of the ten Pikachu you just met. The tables on this site are read straight out of the game's own data, so they hand you the answers before you have found them.
If you have not played it yet, the team's own advice is to go in blind, ideally with friends.
Every wild Pokémon here, by encounter method.
Falkner Gym lists one Pokémon across 3 encounter methods (old rod, good rod, super rod), all at level 5.
Opens up at Fuchsia City, the Safari Zone and the Cycling Road. 2 trainers here:
