0ffice 365

I have following questions.

1) Dir sync is used for migrating user accounts and passwords to office 365.
If we have Dir sync ,and we have on premises 2013 server, can I log in to office 365 and on premises with  same username and password.( Can we have single sign on)

2) If this is true, then why should I have ADFS ?

3) If I have on premises 2013 exchange server and o365 in hybrid mode.

can I route mail flow directly from o365 to outside world instead of routing through on premiss exchange server.

for that any steps needed.
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Vasil Michev (MVP)Commented:
1) If you have enabled password has sync, yes. It's not single sign on however, as you still need to enter the credentials every time you access an O365 resource. "Same sign on" is what they call it, and it's usually preferred for smaller shops. If you are several thousands large, AD FS is the better option.

2) Because it's true Single Sign on, and it offers you more features and control. Check here for example: http://blogs.office.com/2013/07/26/password-hash-sync-simplifies-user-management-for-office-365/

3) You can, but that kinda defeats (one of the) purpose behind Hybrid - having centralized mail flow. It's up to you at the end, you certainly have the option to do so. Go over the EDA, it explains things in details: https://technet.microsoft.com/en-us/exdeploy2013/

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