Hi, Azz—The only sentence of the three that I find somewhat incorrect is (c), and the problem with it could be fixed with a comma after "still." "But" is optional. The basic idea is that he still walks. "With a limp" is a qualifying afterthought:
(c1) He walks still, with a limp.
(c2) He walks still, but with a limp.
There is a subtle difference in emphasis between "He still walks with a limp," the normal sentence, and "He walks with a limp still," which adds a touch of frustration by ending on "still," emphasizing how the limp has lingered.