Hi Alison,
Regarding the Shared mailbox: I recommend you to use the team queue.
About your questions:
1 – Yes you correct
2 – Here are the unsupported email service configurations
Exchange Synchronization
Capability CRM Online
CRM for Outlook, Email Router, or Server Synchronization (if using Exchange Online/O365)
CRM On Premises
CRM for Outlook, Email Router, or Server Synchronization (if using Exchange on premise)
Server-side synchronization doesn’t support the following scenarios:
• Hybrid deployment: Microsoft Dynamics CRM (on-premises) with Exchange Online
• Mix of Exchange/SMTP and POP3/Exchange
• Creation of mass email marketing campaigns
• Extensibility scenarios like extending EWS/POP3/SMTP protocols and creating custom email providers
• Exchange Server 2003 and Exchange Server 2007
• Server-side synchronization in CRM Online, or in a Microsoft Dynamics CRM (on premises) deployment that is configured for FIPS 140-2 compliancy, requires a POP3/SMTP email server that is also FIPS 140-2 compliant. Some email servers are not FIPS 140-2 compliant, such as MSN, Outlook.com, or Windows Live Mail.
3 – I think you need to use the credentials for this shared mail box on the queue, since is pop3/smtp there no other way, unless you have a trust between your AD and Office365 (but i`m not the expert on this area to tell you how)
Since you are using a team queue only the users that belong to that team will see the emails on the queue.
4- First you need to setup up the email configurations to “send email on his behalf”. But if you can be more clear related to this issue you getting I will appreciate.
I hope this helps,