Good, you have a pretty ok understanding of things. So yes the Hayabusa was relatively isolated clan that came from a country called Owatatsumi. There they were farmers/country folks basically but when Kaguya ate the chakra fruit, war started to wage. The Hayabusa throughout the years worshipped three great dragon spirits, who had awakened to protect the clan during those times. However after the wars and such, the dragons gifted the Hayabusa with a unique power for their loyalty towards them and each left a piece of themselves in the clan. So these are referred to as a “Dantian” or simply chakra pools. Outside of your normal chakra system, each Hayabusa is gifted with these three pools which like you said allows us to manipulate the state of existence. This is called Wuji, which the constant state of nothingness in Daoism. Everything in existence came from Wuji, but we as Hayabusa can return things back to that state. Or we can pull them out of nothingness into existence, which is called Taiji.
So now that we went over this, let me briefly explain what each Dantian does and then we’ll go into the clan passives. Each Dantian represents one of the dragons, in which a certain dantian grants one the ability to manipulate the existence of said object based on it. There’s Lower, Middle and Upper. Lower allows you to control anything physical, ranging from solids, liquids gases etc. It also allows you to erase chakra that takes on a physical form such as Water Release, Earth Release etc. Middle is vital energy or energy in general, which covers things like fire, lightning, wind, etc. Upper is spiritual based, allowing you to do the same but on a spiritual level.
Once you understand that, we’ll move onto the passive. Which of the three would you like to learn first? Wujin, Taijin or Spirituality.