chown changes the file owner. chmod changes permissions. So, if a file or directory is owned by root but a user should have access, you could make them the owner or you could keep root the owner and just allow read/write access.

They come up more on servers where you often have multiple users with different access levels. Some users might not have sudo permission but do have full control over their home directory and whatever else they need. And web servers, for instance, will usually have a user called www-data or similar and it’s shared by all the users in the “developer” group.

No, directories without anything mounted on them are normal directories - which checks out, since you can mount anything anywhere; unlike Windows volume letters, which only exist when volumes are mounted or detected by the OS.

When you mount a filesystem onto a directory, the OS "replaces" its contents AND permissions with that of the filesystem's root.

Here's an example with my setup (hopefully you're somewhat familiar with Bash and the output of ls -l).

Imagine some random filesystem in /dev/sda1 owned by "user" which only contains a file named "/Hello World.txt":

$ # List permissions of files in /mnt:
$ # note that none of the directories have read, write nor execute permissions
$ ls -la /mnt
drwxr-xr-x   1 root root          168 May 31 23:13 .
drwxr-xr-x   1 root root          128 May 31 23:14 ..
d---------   1 root root            0 Aug  1  2020 a/
d---------   1 root root            0 Feb 11  2022 b/
d---------   1 root root            0 Aug 11  2021 vdisks/

$ # No read permission on a directory => directory entries cannot be listed
$ ls /mnt/a
cannot open directory '/mnt/a': Permission denied

$ sudo mount /dev/sda1 /mnt/a

$ # List again the permissions in /mnt: the root of /dev/sda1
$ # has rwxr-xr-x (or 755) permissions, which override the 000 of /mnt/a ...
$ ls -la /mnt
drwxr-xr-x   1 root root          168 May 31 23:13 .
drwxr-xr-x   1 root root          128 May 31 23:14 ..
drwxr-xr-x   1 root root            0 Aug  1  2020 a/
d---------   1 root root            0 Feb 11  2022 b/
d---------   1 root root            0 Aug 11  2021 vdisks/

$ # ... and its contents can be accessed by the mounted filesystem's owner:
$ ls -la /mnt/a
drwxr-xr-x   1 user user          168 May 31 23:13 .
drwxr-xr-x   1 root root          168 May 31 23:13 ..
-rw-r--r-- 1 user user   0 Jul  4 22:13 'Hello World.txt'

$ find /mnt
/mnt
/mnt/a
/mnt/a/Hello World.txt
find: ‘/mnt/b Permission denied
find: ‘/mnt/vdisks’: Permission denied

Please note that me setting permissions is just extreme pedantry, it's not necessary at all and barely changes anything and if you're still getting familiar with how the Linux VFS and its permissions work you can just ignore all of this.