Zox and his Gorldtsuikar family have come from Kaizoku Topia (Pirate Topia). They travel to different worlds with their Pirate Ship.
Zox is the eldest son and as seen in his first appearance, he likes to sing.
Flint who is the younger sister of Zox is in charge of creating the Sentai Gears for Zox. She & Zox stole the blueprint of Geardaringer from Tojitendo.
When Gorldtsuikar family traveled to Gokaiger's world, Flint fell in love with their design and thought it was cool. Because of that TwoKaizer looks exactly like Gokai Red.
Kattanaa & Rikki are twins and they are in those mini forms because of an incident which happened when they went to SD Topia. SD = Super Deformed as per my knowledge.
In Kikai Topia, there is a rule to steal. So when Zox visited the shop Colorful and liked the sweets. He stole it.
So this scan over here gives the correct romanization for Zox's name to be 'Zox Gorldtsuikar' & not 'Zox Goldtweaker'.
TwoKaizer's finisher using Geardalinger in Gun Mode is called "Full Power Shoot". Finisher in Sword Mode is called "Hyper Power Cut".