Kouji and Shizuru got together later and started a family of badassesAll their descedants were sharing his Hot Blood and Haminess and her Badassery and Catch Phrase. Last member of their dynasty was Kamina.
Kouji's parents somehow knows Mazinger teamThat's why he's named after Kouji Kabuto and Tetsuya Tsurugi - his parents were their friends. Nicolas Cage could name his son Kal-El then I bet two okatu could name their child Kouji Tetsuya.
Show takes place in one Universe with GaoGaiGarIn episode 2 Go is reading about wedding of "Gai and Mikoto" in the newspaper. While it wasn't ever stated in the show, it's possible that Gai and Mikoto could get married between the events of GaoGaiGar and FINAL After becoming Evolouders. And wedding of guy who defeated Zonder Empire clearly would make it to the front page.
Godannar is the distant past of Gurren Lagann!The Mimetic Beasts and then the Insania Virus were sent by the Anti-Spirals. When THAT didn't work, they decided to take a direct approach.