Short answers, pulled from the story.
Gurren Lagann premiered on TV Tokyo on the 1st of April 2007 and ran for 27 episodes until the 30th of September 2007. The series was directed by Hiroyuki Imaishi and written by Kazuki Nakashima.
Simon is the main character of the anime series Gurren Lagann and is introduced as a timid fourteen-year-old digger from the village of Giha. He discovers a Core Drill that allows him to pilot a Gunmen robot and eventually becomes the leader of Team Dai-Gurren.
Lordgenome is the Spiral King who rules Earth from a palace called Teppelin and forces humanity underground to protect them from the Anti-Spirals. He is a bio-computer resurrected later in the series who was once part of an intergalactic army of warriors.
The animated films Childhood's End and The Lights in the Sky are Stars were released in Japanese theaters on the 6th of September 2008 and the 25th of April 2009 respectively. These films compile the events of the original series with new animated scenes.
The anime series Gurren Lagann influenced the creation of Studio Trigger which was founded by director Hiroyuki Imaishi in 2011 as a successor to Gainax. The show's success and style directly led to the formation of this new studio.