Never herd of wall tiles cracking. If you have access to the underside of the bathroom (via basement ceiling), you may want to check of the wall(s) has proper support for load or a non-supported floor plywood joint may have been installed the wrong way/not supported properly. You should be able to see the nails coming through the floor plywood where the wall(s) is located above. You may have to add blocking and/or brace(s) with joist hangers for support as required. Interior wall studs may also been spaced at 24"c/c instead of 16"c/c if the wall tiles were not installed by the builder not accounting for heavier than normal load.
If by chance the washroom is in the basement::
- Non-load bearing walls (interior non-loading will be supported by the slab.
- Load bearing walls will be supported by footing foundations
As for your toilet moving: the wax gasket may need replacing if not seated properly (rocking). If it just seems a bit loose, try to just tighten the flange bolts on both sides of the bottom of the toilet after removing caps. If no spacers are present between the bolts and the ceramic, they need to be there to not crack the base or reduce the chance of over-tightening that would do the same. There may be water coming from a shower that's close by or from the sweating of the tank in the humid summer months.
If the ceiling are closed for access below, you have the choice of tackling the job from within the bathroom by removing the some of the plywood floor to inspect the problem OR by the ceiling below. I would should the ceiling below if it was me.
Good Luck!
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