How to set a bit stream in mprj (37:0)? How will a user provide voltage values to each of the GPIO pins? Can I load data into m locations of an nxm memory array through GPIO pins ? @Matt Venn

Yes use a test bench to set the gpio pins

Actually, is it possible to write data externally via GPIO pins into user memory once the chip is fabricated?

yes, but you will need some firmware to do that

Yes, you should be able to write to a memory via GPIOs. You can use a simple serial interface such as UART, and a design a host interface on die to decode the commands and consolidate them into appropriate control, address and data buses. And then of course, as Matt mentioned, you can write firmware to configure those pins as ins or outs. There's also an in-house UART capability provided in caravel, but I did not explore that; you might wanna check that out as well.