Even in a fire which caused most of the destruction in 70 AD, there probably were walls remaining. All living in those times was on the upper floor. There are mystics in the Catholic tradition which say that the Last Supper was celebrated in the building above where David is buried. Lots of tradition. And tolerance cuts both ways. I’m sure its hard for the Israelis to accept that David is a key to the RC tradition as well as to theirs.
True.
There weren't walls standing after 132 AD, period. The Jews had another revolt and the Romans very deliberately took apart everything so that there wasn't a single wall left standing in and around that part of the city.
Everything was razed to ground level and the stones buildings were built from were even removed from the area. The wailing wall is actually a retaining wall for the base the Temple was built on.