What should I use as backing for mosaic accent tiles that are a different thickness than the main field tiles?
If the mosaic accent tiles are thinner than the field tiles, I think building up extra thinset behind the accent tiles and carefully pushing them into it so they are flush with the surrounding field tiles is a decent approach.

If the mosaic accent tiles are thicker... I don't have a good solution for that.  That is the situation I had in my shower and I just have a bit of a lip that is grouted.  The transition is not too bad.

How different are the tile thickness'?