SSH is a set of network connectivity tools which encrypts all traffic (including passwords) to effectively eliminate eavesdropping, connection hijacking, and other network-level attacks.
SSH suite usually includes the ssh program which replaces telnet, and scp and sftp which replace ftp.
Linux and Mac computers usually have ssh preinstalled. For free Windows implementations of the SSH protocol follow the link
Yes. Both telnet and ftp require the user to log in by typing a password which is transmitted unencrypted over the network, and could be intercepted en-route by a network eavesdropper. We recommend ssh/scp instead of telnet and ftp for all connections.
It depends. Please contact your Department system administrator. for details.
You may use VNC - a free set of software tools which allows you to view a computing 'desktop' environment not only on the machine where it is running, but from anywhere on the Internet and from a wide variety of machine architectures. A step-by-step howto is available here.
The list of available computers and their ssh "fingerprints" is posted in the password-protected area of the Physics web server.