You have it pretty much spot on, once the Cayenne agent is installed on your Pi, associating it with your Cayenne account, you should be able to view the Pi values you’ve mentioned as well as any added sensor data/widgets from any of the web dashboard or mobile apps.
There may be slight discrepancies in how things display on mobile vs web, but you shouldn’t be missing the bulk of data on the web, or having any stuck widgets like you’ve mentioned on mobile. Do you mind sharing your credentials via PM so I can investigate? You can reset the password if you’d like first via this form: https://cayenne.mydevices.com/cayenne/forgot
As far as the Remote Access feature, yes it should work outside of your local wifi network, it makes a secure VNC connection over the internet, but this broke on fresh installs of Raspbian OS with PIXEL, and we’re working to resolve that bug. For whatever reason, it works OK if you’re on an older install of Raspbian that’s been upgraded to the PIXEL UI – something about the fresh install breaks it. I’ll update on this forum when we have a fix for that in place.