Concrete – How to lay tile backer board on sandy cement floor

• Step 1: Remove existing fixtures (toilet, sink, etc.)
• Step 2: Remove existing tile.
• Step 3: Determine if existing sub floor is appropriate for tile.
• Step 3 a: Replace existing sub floor (if necessary).
• Step 3 b: Install appropriate sub floor.
• Step 4: Install new tile.
• Step 5: Reinstall fixtures.
• Step 6: Enjoy your new bathroom for years to come.

This may not be the answer you are looking for, but to do the job right (in my opinion) you should start fresh.

If you don't feel comfortable doing the job yourself, you might think about hiring a professional.

I apologizes for the bluntness of my answer; as a home owner myself who has had to fix the messes others have created, in my opinion there is no excuse for not doing a job properly and (as Mike Holmes would say) making it right.

Removing the existing tile will cost you nothing but time, and in the end it will make you feel much better knowing that you can enjoy the remodel for years to come trouble free.

Pry that tile up, it sounds loose on that corner - i.e. not only unsupported, but some of the thinset in contact with the tile did not adhere.

That looks like unglazed clay tile (aka mexican clay tile), which you must moisten on the bottom to get it to adhere well. If you don't, the tile sucks the water out of the thinset before the thinset can bond, and you get what you have with that "klonking" tile.

If it was just voids at the corners, you could just "pipe" some more thinset under the tile with a pastry bag, but after watching that video, I would pry up that tile. Hopefully you have some spares.