How do you check if a filesystem is mounted in Linux?

Check /proc/mounts. If you grep on the filesystem name and the path you want it mounted (maybe even a specific line with all options included) you can tell if the filesystem is mounted.

What file systems can be mounted in Linux?

As you may already know, Linux supports numerous filesystems, such as Ext4, ext3, ext2, sysfs, securityfs, FAT16, FAT32, NTFS, and many. The most commonly used filesystem is Ext4.