Supertall vs. Natural Disaster
 

Are our supertall towers capable of surviving an F5 tornado or Mercalli XII earthquake? Or are those examples just too much for human architecture? If so, what level of intensity could they survive?

They wouldn't be built if they couldn't handle the location's natural phenomenon.

I'd imagine that the towers themselves wouldn't fall over from nothing less than a nuclear blast with the kind of concrete these modern towers are built with, but even a relatively frequent category 3 or 4 hurricane would gut a supertall just like any other building. Sandy was nowhere close to a worst case scenario for New York.

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It will be interesting to see how Miami (for example) fares when a Category 5 inevitably does impact it.

As far as natural disasters go. Tall buildings in Tokyo did well considering there was a 9+ quake 200 miles away. Had it been directly under that city. well that would be like a F5 going through Dallas or OKC. Only the steel beams and columns from a tall building would be standing.Tall buildings in most cases can handle it. I guess a ground rupture from a large quake going through a buildings foundation would be the worst situation.

Miami has already survived a CAT 5 when Hurricane Andrew struck on August 24, 1992. What did collapse were Single Family homes built out of Wood Frames which are now banned in Miami-Dade County since then.
Concrete structures did survive but some had their windows blown out.

Cities in Asia face Typhoons of the same category and their buildings survive as well so why wouldn't Miami ?

Has there been an earthquake with a magnitude of 12 at any time in the historical era? I'm not sure we need to plan buildings for earthquakes that happen less than every 10,000 years.

Modern high-rises are built to withstand quakes of substantial power. I think as you get over a magnitude of 9, or especially if you had one over 10, there could be substantial risk of failure for any human-engineered structure. At that scale, it would not only need to survive the forces at the surface, but there could be actually movement differences between the bedrock and all soil on it, putting the foundation at risk. Imagine the forces involved when earth moves in waves like a tsunami, which is what the description of a Mercalli XII quake includes. Building for that sort of event would basically mean we don't build at all. Fortunately, that sort of event is extremely unlikely in even the timeline of the history of most nations.

Nothing close to CAT 5 conditions were experienced in Miami during Hurricane Andrew, because the Hurricane's strong side missed the city by quite a distance. The place that you mentioned (Homestead) did experience those winds though and it was put to ruin as a result.

Tall buildings that experience high winds, like 432 Park, have something called a tuned mass damper at their tops - It's essentially a free-floating weight that moves independently from the structure and counteracts the force of a gust, like a pendulum.

Tall buildings that experience earthquakes usually have several tools at their disposal - One is a foundation that is not anchored to directly the ground, but instead resting on hydraulic or rubber 'springs' that allow the building to absorb quakes. Another is a central beam that moves independently from the more rigid surrounding structure - this beam, which can easily sway several inches at once, acts similarly to the tuned mass damper, absorbing ground shocks instead of wind.

That last technique was first employed in pagodas - you should read about it here!