If I connect to a server via SSH, what network traffic is viewable to someone monitoring the network? For example, if I'm at work and connect to a server via SSH, what can the network admins see? Do they just see the IP and port I'm connected to, but all of the data itself is encrypted? What if I connect to one server, and then SSH from that server to another server - is that traffic viewable, or does it just look like data to the first server?
I want to make sure if I connect to a server as little traffic is viewable to any external parties. Is there any way to hide the IP I'm connecting to as well?
Update Server 1 and Server 2 are both external to the network I'm currently on. Does that change anything in regards to what someone on my network can see outgoing from server 1?