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Can I connect and sync Office365 Sharepoint documents with my loacl Outlook 2010? (Also with iPhone mail etc.)
This is Tim with Microsoft Office 365 SharePoint Support.
It is possible to synchronize you SharePoint Online with a local install of Outlook 2010. From a document library, you can click on the "Library" tab, and in the connect and export area you will have the option to connect with Outlook.
Unfortunately, there is no direct way to synchronize your iPhone mail with SharePoint. You can look into 3rd party application that may be able to help you with the synchronization.
Microsoft Office 365 SharePoint Support