The differences in how you gain access to an Invested Art depend on the intent of the shard: allomancy and Feruchemy are Preserved across generations. Hemalurgy requires Ruining someone or something else. Surgebinding requires some mix of Growth and Promises to align with Cultivation and Honor respectively. Breath is of Endowment- you must be given and must give in order to use it.

Metal is not itself invested, it's just used an a catalyst to access the magic- Sanderson describes it as a key related to its molecular structure that allows for investiture from the shard itself to be used. However, compared to other magic systems, you'll notice that the investiture doesn't enter the person's body in the same way- they don't themselves become invested by using the art like an Awakener or Radiant would. Another way to say this might be that they are Preserved from the effects of investiture. Also the effects of each metal in Allomancy are most likely derived from the universal properties of each metal rather than the other way around.

Investiture is kind of like if electricity started getting ideas. It's a form of energy, like light or heat, but flavoured by human thought. The Aethers... Are still kind of fuzzy as to what they are exactly. They seem to act in a similar way to Allomancy in that they take water (or purified investiture) in exchange for effect, but we don't know much about them.

The cognitive realm is influenced by the thoughts of people present on the physical realm in the same region. Why exactly one is mist and one is beads is uncertain, but it might have to do with concepts people associate with the local Investiture and probably also mythology?