#1 is the degauss coil connector - for the degaussing coil wrapped around the CRT tube itself. That coil should have a matching connector, i would hope. And no, it isn't strictly necessary, but if you don't use it you'll probably want something like a wand instead.
The post for GND is as you suspect. Very important.
As for the other connectors, I would use a multimeter to help narrow things down. Given this is a wirewound transformer, you will be able to test for continuity across the different coils and possible taps. Then you start thinking things through...
I hope that's of some help, at least :/