While the Shihakusho seems in someway intrinsic to Shinigami status (see how Ichigo's conjured it out of thin air thrice now) and clothes are explicitly part of your soul, we've also seen Shinigami swap clothes in their spirit forms, so they aren't a fixed part.

As for fighting in Gigai, casting of Kido seems possible at least. However, Ichigo, Rukia and most others don't have their Zanpakuto available in Gigai (Urahara & the Vizard might be an expection), which is sorta inconvenient. Also, I'd imagine walking through walls is more of a hassle with a physical body, and woe be the poor mortals who see them flying all around.