The first is a triggered ability: "When this permanent enters, target player may search their library for a card named Mothers Yamazaki, reveal it, put it into their hand, then shuffle." The second and third abilities represented by Mothers Yamazaki's "partner with itself" keyword modify the rules for deck construction in the Commander variant and have no function outside of that variant
Each of the brackets is intended to represent a different level of play
You always start the game with your combo piece in hand, and the format has so many threats to cheat in besides the Ripper: Patron of the Vein, Markov Enforcer, and Crossway Troublemakers are just a few of the big vamps that this Rakdos commander puts into play unreasonably early
The real question is how you want to play hyper-aggressive swarms, intricate combo setups, or steady control
Lair of the Hydra Everything that I like about Den of the Bugbear is true of Lair of the Hydra, except that green decks will more commonly be interested in activating the card by their nature in the classic Cube environments