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I am working with the STM32F407 board. Same as the link: https://github.com/mcauser/BLACK_F407VE. Is it possible to use an SD card in SDIO mode? (The board does not support SPI for SD CARD). Do you need to change anything in the FW? I found this link but it doesn't tell me much https://github.com/rusefi/rusefi/issues/683. Thank you.

Yes, the firmware is compiled for either SDIO or SPI. You need to define EFI_SDC_DEVICE when compiling, and configure the pins to the correct alternate function in board.h.

Could you give me a example of code to configure pins in board.h file, please?
I'm novice in programming

http://www.cplusplus.com/ is a great source of tutorials for learning C++.
board.h contains preprocessor directives, so you should read the article on that so you have some idea what you're working with.
There are a lot of board.h files you can look at for examples. I'm not sure if any of them use SDIO.

I think this config does it: https://github.com/rusefi/rusefi/blob/master/firmware/config/boards/subaru_eg33/board_io.h