How best can I real-time (or as close possible) sync my Outlook for Mac (2011) calendar with my google calendar and contacts, and my iPhone/iPad calendar and contacts - which sync well with my google accounts already?

I am a new Mac user, just migrating from PC with 10+yrs of emails in an Outlook .pst file. Hence wanting to start with Outlook for Mac so I can reference old emails. 

The alternative question is whether there is an easy way to import a 5+gb .pst file into Mail for Mac, retaining the folder structure of those emails?

Thanks