Arslan
In another formum I got a partial answer:
In settings > mail, calendar > add a cardDav account using google.com (I think) as the sever.
After I did this contacts added from my laptop to Google contacts are almost instantly pushed down to the iPhone contact list.
UNFORTUNEATLY not the other way around. i.e. Contacts added to the iPhone never show up in Google contacts. Horrible software and support from Apple....