how fast is the process of an Arduino requesting info and then receiving it from the FPGA?
That largely depends on how you do it.
The X02 series has built-in SPI and I2C hardware, I don't know what speed they are rated at but in the case of the SPI port I think "bloody fast" is a reasonable guess.
But if you want really bloody fast then in the case of the SAM (on the Due) you could memory-map the X02 and talk to it at external memory speeds which is probably about 20-30M bytes per second, twice that if you use 16-bit data.
What you do with that data is another question, VGA interface with dual-ported screen RAM anyone?
Apart from all that you can add pretty much any hardware you like for example add a UART and talk to the FPGA using serial. Or maybe just a few 74xx595 shift registers and use shiftOut() to send data.
What are the advantages in using an FPGA vs another Arduino chip/board flashed with the same functionality as the FPGA?
The FPGA is hardware, therefore is an order of magnitude faster than a second processor.
And if all that's not enough you can actually put an 8 or 32-bit processor inside the FPGA as well as other hardware.
These XO2 chips are very interesting, as indeed are all the FPGA/CPLD devices but I like the look of the XO2s.
I think all that's right, please correct me if not Roy.
EDIT: Roy, I backed your project the other day, hopefully it will get over the line.