I will post in a few hours. I will be quite a while...
This extreme server instability is making reading and navigating unreliable; I will post, along with my initiative when I can. It is evident I missed something significant.
In many cases, 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 DM’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.
Riot Weapons.
Implements and tools are equivalent to weapons, and are given stats equal to a similar weapon, as per the PHB, however they lose the thrown tag if the base weapon had it.