Can epoxy grout be used at the joint between the tiles and the metal shower drain?
Or is it better to use silicone sealant there? A similar question about the corner of the wall and the connection between the wall and floor tiles.
You can do this as long as the substrate is solid, and the waterproofing was properly executed and taped.
Wall corners and junctions of wall and floor tiles – if the substrate is solid and everything is sealed, you can do the same.
If it is a plasterboard box or something similar, sealant is better. With grout, even epoxy, it's a lottery. It might crack. But maybe not, it depends on your luck.