I have no clue on the paint and sealer but I would stick with Silicon for the tiles I know that its safe and is moisture resistant. I have a feeling that grout would soak up all sorts of things. There is a DIY section. you might have more luck posting about this there.

just another thought. you might want to leave the tiles separate (no grout or silicone) That way when they get dirty you can pull them out and wash them.