From what I know, the only way to login to discussion.fp.o is using your Fedora account, so that’s the only place you need to update your password.
There’s sometimes a delay in the badges app—lots of badges, and the app is a bit old and takes time to process things. I see someone did get the paranoid panda badge today, so you should really get yours soon too. If you do not, please file a ticket with the badges project and someone can have a look (and award it manually if required):
If you want to see it in discussion, you still have to send a message in this topic:
Just for your information, I already several times changed my password and I never got that badge.
I maybe have to ask if I get it manually from the badge team.