Changed lost account passwords by editing GRUB but still unable to access account? (Linux Mint 18.3)

Question

I have a fresh install of Linux Mint 18.3 (System setup: dual-boot with Windows 10)

I set up 4 accounts:

user_1
user_2
user_3
user_4

I did not write the passwords down, woke up the next morning and couldn't remember any of them.

I attempted to change the passwords for all four users as follows:

(1) Booted my system and when the Grub menu appeared, 
    I made sure my Linux Mint 18.3 OS was highlighted,
    I pressed e (for edit).
(2) Arrowed down to the line that starts with "linux"
    It looks like this: linux /boot/vmlinuz-3.16.0-38-generic, 
    root=UUID=b1bde976-50e2-4c32-a760-17b091b4202f ro quiet splash 
    $vt_handoff
(3) At the end of that line I deleted the words,
     "quiet splash $vt_handoff" if that is there, and put: rw init=/bin/bash
(4) I then pressed F10 to boot. 
     This resulted as a boot into a root shell.
     I did an ls /home and the system outputted the following:
     user_2
     user_3
(5) I entered a new password for both these users as follows:
    passwd user_1 (and when prompted twice for the password, 
    I entered the new password both times)
(6) I then entered the following command: sync
(7) Next I entered the following command: reboot -f

Note: I also did the same as step (4) step (5), step (6) and step (7) for root

At this point I successfully achieved in changing the password for user_1, user_2 and root.

However, I am still unable to login to user_1 and user_4 at the login screen, as I still do not know the correct passwords for these users.

My Question(s):

(a) How do I change the passwords for user_1 and user_4?
    I assume both are administrative users, especially since it is,
    my belief that the first user created after a fresh install is,
    an administrative account by default.

(b) Why when I log in as user_2 or user_3 and do an ls /home does it only show me, 
    the user accounts for user_2 and user_3.

(c) In general, should I only have one admin account on my system?

(d) Does an administrator account have the same privileges as root after,
    (su "ing" subsequent to logging, into user_2 and user_3)  

Answer 1

• The sequence you described is the correct way to reset a password if you lost access to root on the machine. Linux doesn't have a concept of an administrative user besides root, unless you talk about sudo privileges.
• Home directories don't need to be in /home, it is just often done this way. Look at /etc/passwd for the home directories of these users.
• You can have as many accounts as you want with sudo privileges fitting your needs.
• su to user_2 or user_3 only gives the rights of that user, not the rights of root.

Edit

Some additional observations based on the comments and the text in the other answer:

If I select user_1 OR user_4 and enter the same password the system will act as if it is about to login (screen goes blank for 1 or 2 seconds) then returns to the login screen. If I enter the wrong password I will immediately see the error "Incorrect password, please try again".

This indicates that the password is correct and there is something wrong. In general in such cases it is a good idea to try a known wrong password and see whether the reaction of the system is different.

While it is possible to have home directories outside of /home, in your case not only the passwords but also two of the home directories were lost. This was the reason why the login aborted. A message to that effect should have been written to some logfile.

Answer 2

The problem:

Initially I followed the password reset process outlined in the question, this worked for user_2 and user_3 (i.e I could login using the new password), however I was still unable to log in to the the user_1 and user_4 accounts.

I solved this using the following process:

(1) I logged into user_2 using the new password.

(2) Opened a terminal and entered the following command:

su - user_1 

Note: When prompted for the password I used the new password, as assigned to user_1 using the process outlined in the question, and it worked. However the system displayed the following text:

No directory, logging in with HOME=/

(3) I then entered the following command:

mkdir /home/user_1

(4) Following on from this I accessed root privileges using the following command:

su 

Note: Password was the same as set during the process outlined in the question.

(5) Then I did the following:

chown user_1:user_1 /home/user_1

(6) I then closed the terminal session and logged out of user_2

(7) Finally to verify when I ended up back at the main login screen I selected the user_1 account and was able to login using the process outlined in the question.

Note: I did the same for user_4.

I would like to thank @RalfFriedl and @confetti for their input