I'll try to cover as much as I can. The Anti-Spiral dimension exists within dimensions (between the 10th and 11th dimensions), while the Super Spiral Space is described by Final Drill as existing beyond dimensions (I'll try find the quote again). As for where the fist fight between Simon and the Anti-Spiral took place, it technically takes place in both, as the galaxy sized mecha (TTGL & the Granzeboma) are Super Spiral Spaces. Also as a note, even though the Anti-Spiral dimension is still bound to physics, the Anti-Spiral can control how physics work in their pocket universe. Flying, energy blasts and force fields are the easiest ones, as even pre-timeskip Gurren Lagann has those. Super Galaxy Dai-Gurren can travel via warps too (perceptual teleportation), and can even attack enemies in warps outside linear time (Mega-Maelstrom Vortex Cannon). Gurren Lagann can regenerate, although after the battle the damage seems to be restored so it has to be manually fixed. To tie this into...