1) The only way you could do this automatically would be to put the plugin inside an extension and do it with the extension.
2) You can't, since plugins don't know anything outside of the page they are in. You might be able to jury-rig something using an extension, I suppose, but I'm not sure if that's possible or not.
3 and 4) Your best bet is probably to figure out how to get these notifications with javascript and inject javascript that will call back into your plugin.
Sounds like one of your main sticking points is that you aren't clear on what a plugin can do; you may want to read up a bit.