Here are some things that I would double check:
If you register 2-3 test leads with case 2 are the tokens different, they should be unique
Have you checked that the token in the confirmation email doesn't have any anomalies that you can tell?
If you delay sending out the confirmation emails, does anything change? (This shouldn't but you never know if its a timing issue or a race condition)
If you fire off a confirmation email manually and not through a trigger does that work with the token.
It should work as you described. In Case 3 I would not expect that to fire off a confirmation email. That is expected behavior. Without actually seeing some screen shots, it's hard to say. Usually in these cases it's something "minor" that is causing the issue. Go through process of elimination and test every aspect.
The token is pulling the data and URL from WebEx but that URL is wrong. So I don't think firing the email manually resolve the issue. Plus manual email firing of hundreds of registrants is not the way to go. =(
For case 3 - I don't understand why WebEx autoresponder emails are not firing. I've never had that issue with GoToWebinar.