I can no longer login as root user (Raspberry Pi running Raspbian)
Solution 1:
This problem isn't related to the root password, it's related to the shell in /etc/passwd:
/root:bin:bash:
Your shell in /etc/passwd needs to exist, and should match an entry in /etc/shells.
Also, it appears the general format of your /root line is amiss, as it cannot identify the home directory field.
If single user mode doesn't work, you can always boot into some live device, such as USB drive, mount the / filesystem and edit /etc/passwd directly. The root line should look something like:
root:x:0:0:root:/root:/bin/bash