If your notifications aren't working, it appears that having both email notifications and site notifications turned on in the same category will prevent the notifications from being sent out. If you want to help test this, try turning off email notifications if you have them on and see if you start getting site notifications from new replies made after you save those settings. We'll test it on our end as well, of course, and see if we can get them all going out properly.
If your notification changes aren't being saved when you save your settings, apologies: it's a known issue and is being looked into.
Getting notifications for quoting yourself is a known bug that is being addressed.