This is a natural product and therefore some shade differences can occur. This is a characteristic of the product. Tile is 8mm thick with a 2mm tolerance.
Slate is a natural material which is porous and in wet environments such as a bathroom water can be absorbed causing discolouration. To prevent staining the tiles should be sealed by applying a sealant to the surface before and after grouting. This is standard practice for installation of natural tiles.
With all tiles (natural or ceramic), product should be mixed from a number of different boxes before fixing in order to achieve a perfect blend of colour and texture.