Do Firearms (specifically, the firearms from Critical Role's Gunslinger Martial Archetype for Fighters) count as ranged weapons?
Can they be used with the Archery or Close Quarters Shooter (UA) fighting styles?
From the gunslinger on DnD Beyond, under firearm properties, the last sentence reads:
Firearms are ranged weapons.
This means that they work with anything that requires a ranged weapon, including the Archery and Close Quarters Shooter fighting styles.