Dave

I wouldn't go too tight on those joints...3mm will look fine......as for the sealer then try

Lithofin MN Slate Seal .....
A solvent based acrylate sealant that produces a high sheen finish, whilst intensifying and protecting the colours and aids maintenance on riven / rough multi-coloured slate.

Lithofin products can be bought from CTD branches.........

good luck and let us know how you get on.......