Is this a better involution S-Box for the Anubis cipher?
Assuming your differential uniformity and non-linearity figures are correct, then yes, your s-box is slightly stronger against basic differential and linear cryptanalysis.  Although Anubis already was essentially immune to basic differential and linear cryptanalysis.  However your s-box would need to be evaluated against other forms of cryptanalysis (e.g. interpolation, invariant subspace, etc) in order to determine if it was "better" in a more general sense.  It may also be less efficient in terms of hardware implementation than the current Anubis s-box (to invoke another, no-less crucial sense of "better").

Note: The AES s-box is affine-equivalent to an involution (as will be obvious if you think about the multiplicative inversion function), and has a higher non-linearity and lower differential uniformity.  Non-linearity and differential uniformity are the same for all affine-equivalent permutations.  So that should help address your question about the maximum non-linearity of an involution.