Remote X w/ cygwin/x
I'm remotely using my server with cygwin/x, but when I close my window on my remote computer, (i think) it closes xserver on my server and I get logged off and it closes all my running applications. Is there any way to disconnect from xserver without it closing?
The X server is on your local computer. The remote applications connect to your X server. The applications are started from the shell which is from your login session to the remote computer. If you kill that, then of course all the applications die. This has nothing to do with X at all.
The applications run through your remote (client) X server, which in this case is Cygwin. If you want to start sessions that will continue to run on your server you might look into using VNC to connect to the host X server on your server.