I bedded mine on sand/cement with a bit of pva on the backs of the slates. If you're doing a small area then exterior tile cement/grout is easier to use. The default sand down my way is sharp sand, and it is not as workable as builder's soft sand ( the golden brown stuff ), so I struggled a bit levelling the slates. The advice I had was to bed them on a 'solid bed', but that's very difficult as if you don't get the amount of cement underneath the slates exactly right, they'll be too high or too low. I was worried about water getting under the slates in any voids then freezing and prising them off. In hindsight, I live in such a mild area, and there is no standing water problem so I think I worried unnecessarily.
Get all your tiles out, and randomise them to mix the batches, then find the thickest one and lay that first - it will determine the thickness of the bed. If you use sand/cement then use soft sand, and mix in plenty of pva or plasticiser to give a workable mix. Then my advice would be to go for a 'five spot' method underneath each tile so they can be settled easily into place and level. Try ot to leave big voids under any tile. A slope of 1:60 ish should be OK. Finish up with some exterior tile grout. I can't comment on adhesives, I've only used the products I've mentioned.
Andy.