1) Cuda is just Nvidia's "stream processors" like AMD, but AMD uses "open cl" for apps
cuda is supported by more applications than open cl, which is one of the main reasons for people recommending that, both are really good, cuda is just largely supported
2) phsyx is not a special technology, it is just additional stuff nvidia adds to the game and gives developers money for that!!
the actual phsyx in a game is calculated in the cpu! nothing too special about nvidia's phsyx as of right now
3)yes cuda core are physical and exist on the cards, just like stream processors do on AMD