How do I mount a folder from another partition?

Yes but before I go that far, couldn't you just symlink?

ln -s /media/tc1/folder ~/home

This link is just a file that is interpreted. It is automatically permanent (until you delete the file).

Failing that you can use mount as you described but the syntax is slightly different:

mount --bind /media/tc1/folder /home/dvad/home

This is not permanent at all, and will be nuked by a restart. If you want it to persist, you'll need something in your /etc/fstab like this:

/media/tc1/folder    /home/dvad/home    none    bind

If you're trying a mount and it's not working, you should make sure that the block-level device is mounted. You can't directly mount a subdirectory of a partition without first mounting the partition.

An alternative to mount:

bindfs -n /media/tc1/folder /home/dvad/home

Requires sudo apt-install bindfs.

Like with mount, this will be a (non-permanent) actual mount point, i.e. for instance not tracked as only a reference but version-control systems. But like ln -s, it does not require superuser permissions like mount does.

Unmount with fusermount -u /home/dvad/home (or by restarting).