Regarding the relationship between Final Fantasy VII and Final Fantasy X referenced there, it isn't part of Mist and Rain. From the interview translations you can see that it's just a concept they were playing with and liked, and not something they had decided on for sure. Also, it doesn't really work, because Shinra is an Al Bhed, and no Al Bhed are found in Final Fantasy VII.
Materia is very rarely used after FFVII, because, like mako, it takes its power directly from the Lifestream. (FFVII characters may still use magic; even without materia, they should be able to use para-magic like what's used in FFVIII.)