Hey Walters,
I'm a software developer who has worked extensively with THREE.js (a WebGL library for showing 3D models in the browser), and I might be able to help with some of your questions...
I looked at HeroForge and it seems like they have a variety of assets that they can compose together into their models for customization. For instance I clicked on the female half elf and I saw that it loaded half elf ears, half elf hair, half elf face, etc... I think they probably use bones to be able to put the model into different poses and morph targets to allow for slider customization.
As far as 3D printing goes, I'm not exactly sure. They might have taken every permutation of model and made a file with all of the objects (weapons, bodies, etc...) with boolean operations. They might be slowly building that building that library up, by just implementing the boolean operations by hand whenever a new combination is ordered. Or maybe it doesn't matter; I'm not familiar with how good Shapeways is at boolean operations.
All of which is to say that it is probably going to require more up-front modeler work (and I'm not much of a modeler so I couldn't give you an estimate on that), but the developer work wouldn't be too hard. I'm estimating about $5-10k in development costs, plus maybe $25-50/month in server/hosting fees (you'll probably be sending pretty large object files). I estimate it would take about 4-6 weeks. I might be way off though, so I'd have to hear more before I could get a better picture of cost.
Cheers!
Jake
Edit: I just looked at Shapeways' library ShapeJS. This might be useful for the boolean operations required to compose a model for 3D printing. In which case I'm doubtful that you would have to create permutations, or make boolean operations by hand.