When you say "communicates" - what do you mean? Is this just for loading the bitstream? Are you copying data files to the FPGA for it to process? Are you streaming data to it?
When you say "though USB" - what do you mean? Is this via the built-in USB-JTAG adaptor? USB-UART? A full USB device implementation?
When you say "can I load .bin files through ethernet?" - what do you mean? You can certainly copy .bin files to the FPGA, just like you can copy text files, .bmp files, .pptx files, etc. If you actually want to configure the FPGA over Ethernet, that is a whole lot harder. I think you'll need to have the FPGA copy the file to the configuration PROM and then perform a soft-reset to load the new data (or perform a partial-reconfiguration so your ethernet controller doesn't also get reset).
Does the board actually have Ethernet hardware? You can't just connect FPGA pins straight to a CAT5 cable; you need a fair bit of hardware in the middle to handle level shifting etc.
You will need to remove the USB peripheral from the block design, remove whatever is driving the USB peripheral (a processor?), insert the Ethernet peripheral, add something to drive that (possibly also a processor), set up your constraints, figure out how to talk to the Ethernet PHY, etc.
