Now on to jas61292's questions.
What existing Pokémon individually affect the usage of entire types?
Pokemon like Lati@s greatly affect steel-types usage in today's meta. If these dragons (and others) didn't exist in OU, steel-types might see less use since other Pokemon carry ressitances they have and also have better offensive typing. Politoed is another Pokemon that affects the use of whole types. Water-types are obviously affected by the use of Politoed since the rain it brings boosts their STAB attacks and allows the use of abilities like Dry Skin and Hydration. Politoed also indirectly affects the use of types that are weak to Water-type attacks as the rain increases the damage they take and even weakens the STABs of Fire-types.
What ways are there to change a typing’s usage outside of simply countering/being countered by them?
Obviously, the removal of Stealth Rock could increase many types usage greatly. Outside of this, rain as I stated above, affects discourages the use of fire-types since it weakens their STAB attacks. Can't think of anything else right now.
What elements of a Pokémon are most important when dictating how it interacts with other types?
A Pokemons ability is a key part of how it interacts with other types. What if Gastrodon or Shedinja lost their abilities? Gastrodon wouldn’t see as much usage since it can’t deal with water-types as well anymore and Shedinja would simply see no use since it is KOed by everything without Wonder Guard. Movepool is also a factor in interaction with other types. Pokemon with good coverage moves can deal with more types than Pokemon with narrow coverage.
Thats all. BTW new to CAP!