Short answers, pulled from the story.
Gurren Lagann was directed by Hiroyuki Imaishi, a fan of the mecha genre who had previously done animation work on Neon Genesis Evangelion. The series composition was written by playwright Kazuki Nakashima, whom Imaishi appointed after working with him on Re: Cutey Honey.
Gurren Lagann ran for 27 episodes on TV Tokyo and its affiliates between April 1 and the 30th of September 2007, plus two specials. The first special was the uncensored version of episode six, and the second was episode 5.5, a bonus that came with the Nintendo DS game.
Gurren Lagann received an Excellence Prize at the 11th Japan Media Arts Festival in 2007 and won the Best Television Production award at the 7th Tokyo Anime Awards in 2008. Director Hiroyuki Imaishi received an individual Personal Best award at the 12th Animation Kobe Festival, and character designer Atsushi Nishigori won the Best Character Design award at the same 2008 Tokyo ceremony.
The first film, a compilation of the series' initial arc with roughly 20 minutes of new animation, premiered in Japanese theaters on the 6th of September 2008. The second film, focusing on the back half of the series with even more new footage, followed on the 25th of April 2009. Shoko Nakagawa sang the theme songs for both.
As of 2021, the rights to Gurren Lagann are owned by Studio Trigger, alongside Imaishi's other works from his time at Gainax. Imaishi founded Studio Trigger in 2011 after leaving Gainax.
Writer Kazuki Nakashima cited Ken Ishikawa, co-creator of Getter Robo, as a key influence, particularly for the series' escalating scale toward the end. The post-apocalyptic setting drew from Combat Mecha Xabungle, character development paid tribute to the boxing manga Ashita no Joe, and Simon's three-stage arc echoed protagonists from earlier Gainax series including Neon Genesis Evangelion and Gunbuster.