Are all the headlines correct?
Has Pope Francis signalled a change in our 2,000 year-old teaching on marriage?

No, as usual his somewhat imprecise words have been twisted and taken out of context.
Here is a thoughtful commentary on this particular furore. 

We are reminded once again that not every word apparently issuing from a pope's mouth in a media report is official teaching.
Here is a small reminder of why we have a pope. Our church is guided by his official  teaching - guaranteed by Jesus the God-man.