How do I sync friend- shared google calendars?
I have exactly the same set-up :)
Mac, iPhone, iPad and girlfriend. I've got a bunch of calenders, and so does my girlfriend.

In Google Calenders, hover on the agenda you want to share and hit the little arrow on the right. A new menu pops open and select "Share this agenda". Now you can invite other people to this agenda by submitting their e-mail address. And you can give them rights (read, write, read/write...)

I hope this works! If not, please let me know cause it's a delight to work with a Mac, iPhone, iPad and girlfriend. Trust me, I know ;-)

EDIT
To get the agenda of your girlfriend, look for the label "Other Agenda's" on the right and paste your girlfriends' e-mail there. And if your girlfriend has shared her agendas with you, they will appear on yours.