Accessing Public Folders in Hybrid Environment - Shared Mailbox a good replacement?

Exchange 2010 Hybrid with Office 365.
Mail Flows to/from On-Premise to Office 365
Mail Flows to/from Internet to On-Premise/Office 365

My Issue is with Public Folders. We have some SQL Server Processes that Process emails that are sent to a Public Folder.  Messages are Read, The Body is parsed and Inserted into SQL Server and the email is deleted or moved to an Archive Public Folder and then anything older that 2 weeks is deleted.

In a Hybrid setup On-Premise can only see On-Premise Public Folders and Office 365 users can only see the Office 365 Public Folders.

When a Office 365 user sends an email to the Primary SMTP address of a On-Premise Public Folder, the email fails as Undeliverable.  

When a Office 365 user sends an email to a secondary SMTP address  of a On-Premise Public Folder it gets there just fine.

A Few Questions:
1) Why can you send to the non-Primary SMTP Address of the On-Premise Public Folder?
2) Should I still be using Public Folders?
3) Can I setup a Office 365 Shared Mailbox for this Purpose and have both On-Premise and Office 365 users send email to it without the NDR?
4) Using EWS (non Managed) can you Access the Shared Mailbox like you can a non-Shared Mailbox?

Scott TownsendIT DirectorAsked:
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Vasil Michev (MVP)Commented:
Cross-premises PF access is possible, but it requires some configuration. In particular to the mail flow issue, there are some restrictions imposed by the so-called DBEB feature in ExO, you can read more about it and the workarounds here:

In general you should still be able to use the PF solution, but as I'm not familiar with your workflow there might be some other issues with it. Shared mailboxes should work just fine as a replacement, the major problem with them is when you have too many people accessing the same shared mailbox at the same time. Assuming it will only be said app, it should be fine. EWS access is supported with shared mailboxes just fine, but you need to access them as delegate, not directly.
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