I've been creating some of my own tilesets, but I have problems with this particular floor tileset. As you can see, it's transparent and has shadows, but I can't put objects on it. Am I overlooking something?
Your images don't really show what's wrong, and in fact I can't even tell where the images are coming from. Please show the FULL tilesets window so we can see what tab you've got active. My first guess would be that you've got your images in the wrong slots. Floor tiles should go in the A2 slot. Anything that goes on the floor (your chairs) should go in the B-E slots. The help file (F1) has more info on tileset specifications.
Oh....you were right. It was the chairs all along. They were in the wrong slots. Tutorials about custom tilesets always mention the importance of transparency, so I overlooked that.