Ceiling – What are the proper tools / technique to cut ceiling tiles

Look for a "threaded eye nut" with your strength requirements. (Breaking strength =4000 kg usually translates into safe working load of 400kg.) Use a plain threaded rod (readily available in the length you need) and a good sized metal plate as a washer (I'd suggest 100mm^2, ~6mm thick). From the scale of your drawing, I'm inferring that the board you're using over the joists will cross 4 joists and be fairly substantial.

If you're concerned about a lot of swinging (ie, children), then it might be a good idea to place a wide-ish timber (a 2x8 on this side of the pond; is that a 37x180?) snug between the middle joists and on top of the ceiling with the rod running through. A couple of screws to pin it in place would help.

Do you want to have to replace it again if there's ever another leak? If yes, then use another inexpensive paper-and-gypsum-based product, such as drywall, green board, etc. If no, then use cementboard. Maybe overkill, but for a small bathroom the uncharge won't be more than $40 and that stuff can get wet till the cows come home and not complain about it! Once it's up, you can texture it, skim coat it, paint it, or whatever you were going to do to the drywall that you were considering.