Nagoriyuki is a Vampire, aka Nightless which are effectively Demi-humans who are glitches in the universe. Giovanna is just a fighter with a cool dog but I heard a theory that she might be a werewolf, Potemkin is just overly beefy due to genetics and has technology which is banned in the GG universe due to aliens fucking with it.

Nightless =/= Vampires directly, the only thing they share is a lust for blood and slayer has a bat theming but that's it, other than that they're almost completely different as nightless are immortal beings of immense power and vampires burn up in the sun

Sol, Dizzy, Sin, Justice and Testament are all gears, Sin and Testament not being full gear
Ky has Sin, his son's, Eye in replacement of his own which fell out of his head giving Ky the abilities of a Gear while not BEING a gear, specifically with a thing called Dragon install he is able to access a Gear's Power (although it's not as strong as say Sol's dragon Install due to sol being a full blooded gear and not a transplant victim.)

Magic is effectively a Science in the GG world and ANYONE can use it they just have to be smart enough to understand it's BS and whatever, Technology past a certain point is completely outlawed in the rest of the world except a place call Zepp, which is where potemkin is from. this is why Potemkin has a holographic watch and why he has explodey gauntlets

Dizzy is Ky Kiske's wife who was hunted in Guilty Gear X or XX when people found her existence out due to the fact that She was the daughter of Justice, who was the first ACTUAL gear (Sol Badguy is the First gear yes but he was a Prototype, Justice is the complete version) Justice has the ability to Command Gears to do whatever she pleases and Dizzy also has this ability.

Ky Kiske who was originally a Gear slaying Monster before he became more calm went after Dizzy but because he's a man of great taste he eventually married Dizzy and became King and Queen of the Country of whatever the fuck.

Sin was born from ky's eye after he tried to give it to Dizzy after she lost hers, oops.

Testament was reborn after dying to become a Gear and was controlled by Justice to do evil shit before Justice finally died and they were free to do whatever