02 Snaky Search - if a snake cannot touch itself, even diagonally then strictly speaking it can't turn a corner because the cells either side of the corner would be touching each other diagonally.

For this type and the Snake variants used in SVC, the wording is commonly accepted to mean that a Snake can make a turn, its just that another instance of it cannot come back and touch a cell it has already passed (note this prohibits immediate U-turns forming 2x2 areas).

Nurikabe:
Is it ok if one inverse the colours?
(Shading islands and leaving seas white)

This question also applies to Coral and Cave in previous rounds.

Yup, all fine as long as you are consistent in depicting the solution of a puzzle.