Yes, there is a type of pad used exclusively for tiling over a concrete floor or over uneven subfloor. The pad stops cracks in the concrete from telegraphing through and eventually causing tiles to pop up or he grout to prematurely erode away. A cork pad is just 1 type of padding material used for this type of application. The pad is first bonded to the sub-floor with thinset, then the tile is laid in a thinset bed atop the pad.
Epoxy grout does not "give". Epoxy grout is exactly what it sounds like. It's a chemical reaction between two chemicals, and most companies use aramid fibers added in the mixture for strength that's almost indestructible. You have to work very fast with epoxy grout: you have about a 20 min working time after mixing it and the more it's mixed the shorter the working time gets. Plain epoxy grout is smooth, but you can get a sanded version. You literally have to grind out epoxy grout with like a Dremel, while normal grout is a variation of Portland cement that can be scraped out with a knife.