Thanks Lawliet. OWA works fine on my iPhone and my iPad, and Outlook 2011 works fine on my Mac. The problem with One/SkyDrive is that evidently there is no Pro/365 version for Mac yet.
However, I did try Document Connection just now for the first time. It asks for a Windows Live ID, which I do not have (for business). When I try to use my Office 365 ID and password (which works for accessing my SharePoint account via the 365 Web portal) I get the message "You do not have permission to connect". So, how do "connect to the Share Point Site by using the Office 365 credentials" per your post?