root vs normal user
 

root can kill any program run by any user. Is it possible for a user to kill another user's program without using sudo, etc. ?

Example: How can make user foo kill program x which is run by user bar ?

1. No.

2. With su or sudo.

By default a user has access to work inside his/her home directory and it depends on program which the user wants to access

But above all it is the super root user which assigns permissions and passwords so even if the user wants to access root files or other user's files it will prompt for a password.

If both users have the same uid then one user can kill programs from the other user. Systemwise there is only one user, but userwyse you will see two separate users.