I think, Microsoft uses claim based authentication for trial version of SharePoint online by default but it might be possible to use Form Based Authentication in Dedicated O365. I need to test or write application to authenticate users for SharePoint online which may have claim based or form based authentication. so Is there any way to create SharePoint online site that uses form based authentication? Or Is there any SharePoint online test site for this?
I have one more question: In SharePoint online, I have invited one external(hotmail) user. I wanted to know details steps on how the external user is authenticated?
Thanks