I think the first time you are trying to mount the drive and not the partition “sudo mount /dev/sdc /mnt” and on the second and third attempt have the sdc1 right, but need to make a folder under mnt to mount the drive onto. Make a folder like ‘tempdrive’ under /mnt and then try it with this since you said it was an ext4 filesystem. Note, you can name it whatever you want I just picked that as an example:
cd /mnt
sudo mkdir tempdrive
sudo mount /dev/sdc1 /mnt/tempdrive
If it doesn’t recognize the filesystem then use -t
sudo mount -t ext4 /dev/sdc1 /mnt/tempdrive
And yes, once you get it down, an fstab entry will make this mount every time, but I would use the uuid in the fstab. I have two mounted on a machine like this in my /etc/fstab: