If the window is popping up and going away, it's usually one of 2 things:
1. The Logging in Popup isn't working
If you have the 'Show 'logging in' Popup' setting enabled in the Configuration -> Facebook area, you need to make sure jQuery and Bootstrap Javascript files are properly loading in your site. I'd recommend:
a) Disabling that setting, or
b) Ensuring the "Load jQuery/Bootstrap" setting is enabled in the Configuration area
2. Your Facebook app is in sandbox mode / not enabled
Please go to the
Facebook Apps area
and make sure that either the "Sandbox Mode" setting is Disabled or the large "Site Online" switch is 'On'. It's the same setting, but shown differently based on various factors.
Regarding the Unsupported feature message, I've never seen or heard of that before. Can you:
a) Let me know a site where we can test
b) Try with Safari on the iPad and see if the same issue occurs. That will help narrow things down.
Thanks,
Alex