[SOLVED] How to properly shutdown a raspberry pi with raspbian?

From my ubuntu PC in the home network, I make

ssh pi@192.168.178.50 sudo shutdown -h 0

then it ask the password "pi@192.168.178.50's password: "
then I take later the connector away from the raspberry pi.

For making it easier for my family members, I was thinking about using an alias
alias stopsmallpc="ssh pi@192.168.178.50 sudo shutdown -h 0"
But
a) the password has still to be given
b) the connector has still to be taken away before the raspberry light is off

Know somebody a solution for a) and/or b) ?
For a), how to give the password into the ssh command line?
Perhaps the raspberry pi LED-lamp cannot completely be shutdowned when it stay at the electricity?

a) maybe sudo visudo will help ?

"sudo visudo": what would be the full syntax? I dont fully understand.
Or perhaps, is it possible to de-activate the password questioning of a SSH line command? (according ubuntu SSH explanation it could be possible with changing the /etc/ssh/sshd_config of the server ?
"PasswordAuthentication no" or other). I would like to have a robust answer before I am messing up my whole home server installation.

sorry, i think there are 2 issues here.

the first is setting up private key encryption:
www.linuxproblem.org/art_9.html

Whatever the shutdown command of the raspberry pi is, my family take the cable away when they dont need the printer anymore. So, I could have 2 solutions:
1. find a hardware "button" and motivate the family members to push it before they take the cable away. I will search such hardware: if I cannot find it? I will buy another SD card when it is destroyed by the wild deconnections.
2. create an icon on windows and ubuntu 12.04 and.. where the command line "ssh ..." is working in the background.
I am searching for 1 due to the amount of pc connected to the raspberry pi server (and where icons should be made..).
So, I close that question.