Hi Richard,
I understand that you want to transfer the data from Outlook for Mac 2011 client to Outlook for Mac client. Generally, if you set up the Office 365 account with Exchange connection type, we don’t need to transfer the mailbox’s data manually. The data will be downloaded automatically to the new Outlook for Mac client with Exchange connection type. Therefore, if you want to transfer the data between Outlook clients, it should be a specific Outlook client side behavior.
I will try my best to answer the questions for you.
Regarding Q1 and Q2 and Q5, generally, if you set up the account with Exchange connection type, it won’t loss emails. And you don’t need to move the public folders manually. Moreover, the account will work well on the iPhone if you set up the account with Exchange connection type.
Regarding to Q4 and Q5, they are specific client side questions. In our forum, we focus on the issues on Office 365 online services. Therefore, I recommend you post the issue in Outlook for Mac forum for dedicated support. Experts in that forum can provide more help. Your understanding is highly appreciated.
Best Regards,