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DP Tiling
A cement based backer board and a proper tanking agent is the only answer here, the mapeilastic aqua defense is great stuff, be sure to use the mapeband around the internals too.
Slate will need to sealed with an impregnator regardless, however, due to acidity/alkalinity of rain water it needs quite a bit of maintenance in that it wears a lot quicker.
Regarding the adhesive and grout, I personally would go for Keraquick and latex plus it is very well suited to external use and it's low water content and rapid hydration makes it ideal for porous stone also it is the same manufacturer as the tanking agent and eliminates risk of chemical incompatibility. Probably wouldn't go to an epoxy grout as I can see it being difficult to fully remove haze from slates textured surface.
Slate will need to sealed with an impregnator regardless, however, due to acidity/alkalinity of rain water it needs quite a bit of maintenance in that it wears a lot quicker.
Regarding the adhesive and grout, I personally would go for Keraquick and latex plus it is very well suited to external use and it's low water content and rapid hydration makes it ideal for porous stone also it is the same manufacturer as the tanking agent and eliminates risk of chemical incompatibility. Probably wouldn't go to an epoxy grout as I can see it being difficult to fully remove haze from slates textured surface.