No minigames, but there's sidequests, specifically, one sidequest consisting of 64 mission monsters, kind of like the Mark system in XII, many of them harder than the final boss.
Also a regular monster you can fight that is harder than the final boss.
Well, there's a pseudo-esque minigame, like of like Chocobo Hot and Cold, that's on Pulse.
And yes, there's a Cid.
There's cities/towns, but generally you're not there for R&R, and most have enemies in them.
There's plenty of weapons, there's 8 tier 1 weapons for each character, ultimately upgradeable to tier 3, or ultimate weapon level.
Depending on the base weapon your ultimate weapon's stats change, so 8 variations of each characters ultimate weapon.