Getting rid of a bookcase is probably not a good idea - if it is properly filled with books it is an ideal absorptive and diffusive surface/cavity with variable frequency response - each book is a different height and different width (and different mass) causing there to be multiple resonant freqs for absorption and diffusion....
The sink is an issue only at the level of the materials and any reflections that it may encourage. The tile has a similar issue - it is my guess that neither can be removed and must be left where they are (simple mechanics really) some rearrangement of other things may help, but there is not much space to move the collapsible wardrobe or anything else to.
Floor layout in terms of a floor plan is going to be far more informative than photos, which may distort locations.
A room impulse taken at different listening points will also help.
The cause of the bad flutter echo is the parallel surface of the ceiling and the floor.