So I know this is an old thread but I'll still post in case someone else needs help but 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 popping up the tile or causing the grout to premature erode away.  A cork pad is just 1 type of padding material used for this type of application. The pad is first thin set to the sub-floor then thin set on top of the pad then tile on top.

Epoxy grout does not "give". Epoxy grout is exactly what it sounds like. It's a chemical reaction between two chemicals with most companies use a Kevlar-type material 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 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.