The key to this answer is in the rule about treating improvised weapons as normal weapons:
At the GM’s option, a character proficient with a weapon can use a similar object as if it were that weapon and use his or her proficiency bonus.
If a character proficient with a weapon can do something and you aren't proficient with a weapon, you can't do that ...
Firearms are Martial Ranged Weapons
The table on DMG, Page 267, shows that the firearms are Martial Ranged Weapons. See also the Hand Crossbow and the Long Bow: Martial Ranged Weapons. (PHB, p. 149).
To use them with proficiency bonus requires being proficient with
martial weapons. If you apply the normal rules for weapons in the
PHB, you can use them ...
At level 11, druids get the class feature Druid Weapon Expertise, giving them expert proficiency with unarmed attacks and all simple weapons. If they want expert proficiency in a martial weapon, taking the Fighter Dedication and Diverse Weapon Expert archetype feats gets them expert proficiency in all martial weapons.
Possibly a special bonus, but most likely an error.
I have looked through the Monster Manual, and have found nothing to explain why the Night Hag has a +1 to each of those skills, aside from this text
A skill bonus is the sum of a monster's relevant ability modifier and
its proficiency bonus, which is determined by the monster's challenge
rating (as ...
If someone with the Tavern Brawler is wielding an Improvised Weapon that a GM may allow to be used proficiently with some weapon proficiency per this rule:
Often, an improvised weapon is similar to an actual weapon and can be treated as such. For example, a table leg is akin to a club. At the GM’s option, a character proficient with a weapon can use ...