There is lots of wood in that stone building. Lots.
Also, high enough temperatures can change the stone. I’m not remotely a material scientist. I vaguely remember stone barbecue pits require some special consideration.
There are also probably concerns about thermal expansions as well. The stone might resettle a little bit differently.
At high temperature some types of stone explode or at least crack.
Yes. If the fire gets deep into the walls it can severely weaken mortar or even crack stones.
especially when water hits the super-hot stone. Hannibal crossing the Alps thing
The melting point of marble is 800ºC and if reports are true that it's a construction mistake and not something more drastic it stands a good chance of not collapsing.
You can cause a drinking glass (melting point 1400C) to explode if you expose it to 100C and 0C water in quick succession. Differential heating, moisture vaporizing, and expansion/contraction are larger concerns than the stone becoming lava.
Yes. Keep in mind that a lot of the wood is structural too (i.e. the roof). It's conceivable that this could cause collapse of some to all of the building.
Definitely. There is a great book called Pillars of the Earth where a cathedral in England burned down in ~1150.