As you say the slate is different thickness's (uncalibrated),i would grade it first,wash it down with water and seal with HG sealer before fixing and once fixed before grouting.I would back butter the tiles and comb the walls with adhesive.You will probably get a rough looking natural wall as the tiles are of different thickness and slightly different sizes,dont use spacers and as there is a lot of work invoved i would charge around £35 m2 but its up to you what you charge ,all the best.
