I will try to give you some help.
I cannot answer the second question, because I don't know the IGES or STEP file types very well, at least at their "DNA" level. In fact, I can't say that about any software or file types that I use. I basically just use software and hardware, I don't do any development.
I can say, about your first question, that what you are essentially talking about, whether you've thought of it this way or not, is reverse engineering. That's what the procedure is called when you have an STL mesh, and want to end up with a hard CAD model. STL mesh is a large collection of triangles that create a 3D shape. You may have found this file on the web, or you could have 3D scanned your file, from a solid object. It looks like you have found your 3D file of a shirt and tie, am I correct? I say this because it's perfect, and it looks like a modeled 3D item.
Now, the hard part. I hate to tell you this, and I have asked this many times, but creating a STEP or IGES is usually not simple from this point. You need the right software, such as Design X Geomagics (now sold by 3D Systems at $30,000) or SpaceClaim, sold by Ansys at around $5000. Massive prices aren't they? I use both at times. I also have some luck using Rhino 3D, as I can import a mesh (STL) file, and build solid geometry in the same XYZ space. But, Rhino is not a true reverse-engineering software, and you can only build something that is sort of close to your original shape. In your case, the file appears to be very organic, with tons of challenging curves, so Rhino would not work well.
A real reverse engineering software does many things, including create complex, curved surfaces, that snap themselves to your STL geometry. That's the real magic formula about rev-eng software packages.
If you are fairly gifted at 3D modeling, you might try Rhino, which is a free download (it only saves 25 times until you then buy it, at roughly $1000US).
I wish I could give you simpler news, but you have embarked on a challenging mission, and I don't know of any free software that truly reverse engineers.
Good luck Matt.
Tom Kay, Ottawa.