I did a cave structure with bits of red shale. First thing I did was take a dremel tool (basically a motor spinning a rotating cylinder of emery stone) and grind all the edges smooth. The next thing I did was take a shower as I was completely covered with brick colored dust. Then I laid out the cave the way I wanted it, then piece by piece set it aside, then rebuilt it with aquarium sealant to hold the pieces together.
If I were doing it again, and I wanted multiple stories, I'd seal together one level at a time, let it cure for two days, and move on to the next level. Also, if I were doing something with a cantilever, like that three story cave you have there, I'd use aquarium safe epoxy i I could lay hands on it, and make sure I had it well supported as it dried.
SO the main things to remember: 1) Smooth edges only, 2) Let your adhesive dry fully, 3) Do it in steps so that the adhesive is firm before you put pressure on it. 4) Be careful moving it into the tank!