Does melting microwires cause internal shorts
you can melt the microwires attaching the wafer to the package


Sure but if that is happening, you're using the chip in the wrong way.
The bondingwires shouldn't get that hot. Solve it by using more in parallel (to more package pins) and/or use thicker bondwires.


  When this happens, can the melted microwires cause shorts between the pins of the chip


No, that should not happen as the bondwires aren't "floating in air" there is material (usually plastic or epoxy) in between the wires.

The scenario you describe isn't the normal usage scenario for an IC, you're purposely damaging it.