XPS is extruded polystyrene; blue or pink board. The less dense "styrofoam" stuff is EPS, expanded poly. XPS is generally preferred below grade, as it is water proof. That said, PassivHaus houses use as much as 16" of EPS under slabs. I would never use EPS underground. On your bubble-stuff under the slab, I humbly suggest that you reconsider that. It is regarded as pure garbage on a few science-related building forums I read. I would refer you to places like greenbuildingadvisor.com, buildingscience.com, healthyheating.com, etc, to see what they think of it. I can't speak for the PEX size, but I hope you've done at least a rough heat loss analysis. There are several available on-line, and all you have to do is plug in your specs; sizes of things, R-values, heating degree days (probably around 8,000 in Illinois), etc. No engineering required. The ones I've used on-line, IMO, are close enough and you likely don't need a pro to run one. Everybody uses the same equation, and this is for a garage.
