At this time 'armed & armored' laws are pretty lax... most people are at least lightly armed & armored (maybe a cloth or leather jacket, with at least a dagger). Gentlemen might carry a swordcane or hire ruffians to provide protections. Others rely on their 'magics', etc.
The regular cops are fairly poorly funded but they still probably wear leather armor and carry a sword and dagger. Those that can afford buy their own revolvers. They can call in special teams that are better armed and armored for certain situations, etc.
For knowledge about Miss Dianna Byrne, Giuseppe would probably use Streetwise as she is not a noble... and a 16 would not get you much. The Mile End Newtown neighborhood is fairly middle class, mostly 'new money' types like low-end industrial engineers, artificers, steam workers, etc.