Best way to do some tile floor repair
My experience has shown me if the mortar is crumbling and tile cracking the base is not thick enough to start with. Even a perfect mix cannot stand up to flex! 

In existing structures my normal plan is to remove existing flooring. Next I put down backer board first with thinset under the backer board and screw it down. Next I put the tile down again with thinset, the additional level of backer board with thinset on each side has not failed be in 40 years, 

First I must say I check the Base , if I walk on it and it feels solid I STILL add the backer in most cases. I am 6’5” and a big guy and at 250 as a skinny guy if I see or feel any flex I add structure and that is the reason I have not had a tile failure similar to yours. 

I can say most DIY tile jobs that fail because the base ( sub floor two thin, no backer) mixing is easy , if two wet it is not as strong  and ends up two thin.  but not usually a problem, under mixing with dry clumps is really to spot as big chunks flake with no base problems. 

I would be looking at the base on a first floor and especially on a second floor with the problems described.