How can I know if a partition is mounted or unmounted?

The mount command is the usual way. On Linux, you can also check /etc/mtab, or /proc/mounts.

You can also use df, which will give you a nicer printout and show the disk usage of the mounted file systems:

$ df -h
Filesystem      Size  Used Avail Use% Mounted on
/dev/sda3        27G  8.6G   17G  35% /
dev             2.0G     0  2.0G   0% /dev
run             2.0G  488K  2.0G   1% /run
tmpfs           2.0G  456K  2.0G   1% /dev/shm
tmpfs           2.0G     0  2.0G   0% /sys/fs/cgroup
tmpfs           2.0G  738M  1.3G  38% /tmp
/dev/sdb2       715G  515G  164G  76% /home
tmpfs           396M  4.0K  396M   1% /run/user/1000

lsblk is a nice way for humans to see devices and mount-points. See also this answer.

$ lsblk
NAME            MAJ:MIN RM   SIZE RO TYPE MOUNTPOINT
sda               8:0    0   7.3T  0 disk
└─dataGB-dataVB 253:1    0  14.6T  0 lvm  /mnt/dataB
sdb               8:16   0   7.3T  0 disk
└─dataGB-dataVB 253:1    0  14.6T  0 lvm  /mnt/dataB
sdc               8:32   0   7.3T  0 disk
└─sdc1            8:33   0   7.3T  0 part
  └─dataG-data  253:0    0   7.3T  0 lvm  /mnt/data
sdd               8:48   0   7.3T  0 disk
└─sdd1            8:49   0   7.3T  0 part
sde               8:64   0   9.1T  0 disk
└─sde1            8:65   0   9.1T  0 part /mnt/dataC
nvme0n1         259:0    0 232.9G  0 disk
└─nvme0n1p1     259:1    0 232.9G  0 part /

findmnt is useful for scripting or to query a specific device:

$ findmnt /dev/sde1
TARGET     SOURCE    FSTYPE OPTIONS
/mnt/dataC /dev/sde1 xfs    rw,relatime,attr2,inode64,noquota