I would like to know what the file system (FAT32, NTFS, exFAT) used by my SD card is, in chrome os.
Using developer mode, "shell" in crosh (ctrl+alt+T), type
mount after you have plugged in the sd-card, and look for
mmcblk0 is internal emmc "disk"). Each line has "type" listed.
Tests show ChromeOS formats SD cards to FAT32 only, other partitions will show (if driver is present), but are not usable by ChromeOS User (but are usable from "crosh> shell" in developer mode)
If you meant the internal emmc,
/ (/dev/dm-0) is read only ext2 and
/dev/mmcblk0p1) is ext4.