Mechanists are a brand-new job "invented" in Ishgard as a way to produce their own tech/magitek for use against dragons, inspired in part by the Garlond Ironworks. The gem you're given is unique in that it's devoid of the etchings described in every other jobs' soul gem since you're the first to hold it, and after each job quest where you learn a new skill, you're implicitly taught by the NPCs, not by the gem giving you knowledge.
I don't think we have lore on the manufacture of firearms yet, unless new BSM quests go into it. We can infer a few things though, like since Limsa has been using muskets and rifles since 1.0, they would know about making them. Ishgard's efforts seem to be largely on the part of just the 1 house the NPCs come from (I'm at work and can't check which house it was, though).
I don't think we have lore on the manufacture of firearms yet, unless new BSM quests go into it. We can infer a few things though, like since Limsa has been using muskets and rifles since 1.0, they would know about making them. Ishgard's efforts seem to be largely on the part of just the 1 house the NPCs come from (I'm at work and can't check which house it was, though).