My bathroom door has a marble door sill, which turns out not to be affixed to anything, so that I can move it freely. (See photos.) I imagine that I ought to fix this. What should I use?
Mix up some thinset mortar and spread out out evenly and then place the door sill on top... Try to even out the area between the sill and the tile as it looks uneven from the photo. The sill can be a little bit slanted to even off the edges of the tile and wood floors. You can fill in any cracks or spaces with the thinset too.