- With a modern version of
mount the file-system type should not need to be specified.
sudo blkid displays label, uuid and type (and
lsblk to display capacities)
file -s /dev/sdX# does the job for partitions as well as disk images.
ls /sys/block/*/* is a good resource for many things (but not determining filesystem type)
I assume this is an embedded device, otherwise you should be taking advantage of coreutils, util-linux, etc. rather than busybox.
Let me make this clear, busybox is not consistent across the board - various vendors strip out commands or cripple them to varied degrees. That said, blkid should be available. Run
busybox --help which will list the commands compiled into the busybox binary. Also note that often not all those symlinks will exist, so you may need to create them as needed.