Linux on the cores .. full access to files ... I think so ... I've created files, written to them, read from them. If you come across limitations, let us know.
RCCE users operate with one RCCE process per core, and that is its intended operation. Having said that, I don't see anything inside RCCE that would prevent you from running more than one RCCE process per core. It's a change to the usage model, but may be worth trying out.
The addresses in the LUTs are physical addresses.