I think the OP's confusion is based on mis-interpreting what was probably said about "sister-resorts" and pool hopping.
There is no pool hopping allowed at Disney resort (I'm ignoring the DVC Member rules, which is an entirely different discussion), but generally it *is* allowed among "sister resorts". That means Riverside and French Quarter and free to use each others pools, and the three All-Star Resorts are free to use any of the other All-Stars' pools.
But that does *not* mean that POR and POFQ can hop to the All-Stars. They're not one large group of sister-resorts, just within their particular grouping.
And while the two halves of Pop Century would have been considered sister-resorts if both halves had been built as designed, Pop Century and AoA are two separate resorts and are not considered "sisters".
As for the food court, you should be free to visit it and buy food there, just like you can go to the restaurant of any Disney hotel and eat there.
-Rob