These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Name Fan: Captain Osaka is a good example of this. DOUBLE K is very famous in the Gurren Lagann fandom, having been discussed briefly in The Escapist magazine, inspired several cosplay groups, and generally having been enjoyed by more or less everyone in the English-speaking fandom (and even outside of it, since it's damn entertaining and funny in its own right, and one doesn't at all need to have watched the anime to like it).
He's also had a single-volume manga published in the past, called Atomic King Daidogan, which is itself heavily inspired by other super robot series.
Crazy Awesome: Kamina, to absolutely nobody's surprise. For reference, his game plan usually goes a little something like this:
The Woobie: Simon, to an extent. He starts to become this when chief Genome reassigns him to work alone, but he really starts to become this when Kamina untacktifully announces that Kittan is "The Raddest Dude on the face of the Earth" and starts spending time with him.