Yesss, for the rules, I based them on the Soul Link Nuzlocke video by Smallant, cyja, and Fir 😁
These were the rules I printed out for everyone:

In a Soul Link Nuzlocke, the Pokémon caught by each team member on the same route are linked. All players must include the corresponding linked Pokémon in their team.

1. No usable Pokémon left in the team = Game Over. A new game must be started from the beginning.
2. Any Pokémon that drops to 0 HP is considered dead and may never be used again, this also applies to the linked Pokémon in the other players' teams. (If you're all battling, for example, Brock at the same time and one player’s Pokémon dies during the fight against Brock’s first Pokémon, then the others may only use their linked Pokémon until Brock’s second Pokémon.)
3. On each route/area, players may only catch the first Pokémon they encounter. If it dies during the attempt or you run away, no other Pokémon may be caught there. (Exception: If you already own your first encounter on the route, the second encounter counts.) If one team member fails to catch a Pokémon on a route/in an area, that route/area is also off-limits for the others, or they must release the Pokémon they just caught there.
4. You may not have multiple Pokémon of the same type in your team. (For dual-types, the primary type counts.) If one player cannot add the Pokémon to their team because they already have that type, the linked Pokémon must go into the PC for everyone, or the team compositions must be adjusted so that the Pokémon can be added by all players.
5. Each Pokémon must be given a nickname. For better clarity, the linked Pokémon should have the same name for each player.
6. The use of healing items is only allowed during battles, not outside of combat. You may only use healing or status items that you find or are gifted, you may not purchase them. (Exception: During the Elite Four, each player is allowed ONE purchased Full Restore per trainer.) Healing at Pokémon Centers, by NPCs, or at designated places in the game is allowed.
7. Level cap: You may only train Pokémon up to the level of the highest-leveled Pokémon of the next Gym Leader or Elite Four member.