When you boot your machine, the system detects partitions on the block I/O devices and automatically starts the appropriate filesystem for each partition.
You aren't likely ever to need to stop or restart a block filesystem; if you change any of the filesystem's options, you can use the -e or -u option to the mount command to update the filesystem.
If you need to change any of the options associated with the block I/O device, you can slay the appropriate devb-* driver (being careful not to pull the carpet from under your feet) and restart it, but you'll need to explicitly mount any of the filesystems on it.
To determine how much free space you have on a filesystem, use the df command. For more information, see the Utilities Reference.
Some filesystems have the concept of being marked as "dirty." This can be used to skip an intensive filesystem-check the next time it starts up. By default, when you mount a filesystem as read-write, that flag is set; when you cleanly unmount the filesystem, the flag is cleared. In between, the filesystem is dirty and may need to be checked (if it never gets cleanly unmounted). The Power-Safe filesystem has no such flag; it just rolls back to the last clean snapshot. You can use the blk marking=none option to turn off this marking; see the entry for io-blk.so in the Utilities Reference.