IGBT = insulated gate bipolar transistor. They are a hybrid of bipolar transistor and field effect transistor. They are used because of the high current, high voltage ratings and fast switching.
Yea, I know what you mean about not finding the information you are looking for on the web. The web has its limits. Induction inverters are a more obscure technology for the hobbyist. Lots of simpler circuits available with good explanations. But for something that is more complex, difficult to build, hard to implement, high power, prone to failure, more expensive... the web has its limits. It could be the people building induction inverters on the web have little knowledge themselves, or are just too lazy to detail everything or assume other people know what they are talking about.
I spent some time looking for a design for a variable frequency drive. VFD shares some characteristics (in a rough sense) with induction inverters. But there really aren't may people on the web building VFDs and publishing all the details. I still want to build a VFD, so the only thing I can do is research the basic theory and start designing. If a "canned" solution for what you want is unavailable, you have to design and build it yourself. If you are really interested in researching, then visiting a good college library would help.
At some point you will have to know how to design something and have a good sense for what is reasonable. At least have enough knowledge to get in the ballpark. A 5 Henry coil is a huge amount of inductance, for example. Maybe useful as a 60hz power supply ballast.
One idea for you: Not sure if it would work, but there are cheap induction cooktops, ~1500 watts, made in China, of course. You could probably buy one of these for about $100. Hack it to your own purposes. Rewind the coil, if necessary, to a shape that can heat your iron rods. I won't say this would work, or that it would be easy, or if 1500 W is enough power, or it won't fail. Its one possibility.