You can easily verify whether an ADFS implementation is working by using a browser and trying to log on:
Replace adfs.yourdomain.com accordingly.
Note that in 2016, this no longer works unless you re-enable this feature through Powershell:
Set-AdfsProperties -EnableIdpInitiatedSignonPage $true
Microsoft has released the Azure Active Directory Connect to the general public. Azure AD Connect replaces (although "incorporates" is a better word) DirSync as the new tool to set up synchronization between your on-premise Active Directory and Azure Active Directory, including Office 365.
The current version of Azure AD Connect is only the beginning. Microsoft has announced a lot more features, which will be made available in the next versions.
More information and installation resources: https://azure.microsoft.com/nl-nl/documentation/articles/active-directory-aadconnect/
As you probably already have noticed, does Outlook prompt for credentials when configuring Outlook for use with a federated Office 365 account, regardless of whether you've set up your intranet zoning for your ADFS server in Internet Explorer options.
Apparently, this is unresolveable as Outlook (2013 and earlier) simply does not support SSO. It is currently unknown whether a subsequent version of Outlook will have this feature.
Oddly enough, Lync does support SSO.