I most recently stumbled upon this. I was wondering, what gauge is the wire and what AC specs are required to achieve that? Voltage, amps, and Hertz wise

 

See this thread.
http://forum.allaboutcircuits.com/threads/feeedback-on-royer-hf-heating.101240/
Induction heating.
Max.

 

If you want to melt screws with an induction coil, and want the lazy solution, look up tesla power supplies on ebay or some such. Here's one example:
http://www.ebay.com/itm/1000W-ZVS-L...568?pt=LH_DefaultDomain_0&hash=item1c440fd900

You supply 24VDC at 20 amps, a loop of copper tubing connected to a water source, and it's watch out screws and bolts!