Is my plan for embedding a mirror in a tile wall ok?
Mirrors get broken.  Mirrors lose their silvering on the back.  Neither is a likely event, but in this case a very expensive or time consuming one.  As a general rule I hate to create situations where fixing it later is difficult. 

For this reason were it my project:


Don't attach the mirror to the substrate with adhesive or thinset.  I don't know what the chemistry between either and the thin layer of aluminum on the back of the glass would be. If you do removing the mirror will be difficult.
Buy a mirror with holes drilled in it.  Buy a set of the cute rosettes and attach the mirror directly to the wall.
Frame the mirror in a complementary wood, and attach THAT to the wall.  The outer edge of the frame should be raked about 5 degrees so that it can be removed from the tile when necessary.