How do I get my GPS working in Android 4.1 Jelly Bean?
Have you tried GPSFix kind of apps from Play store? 

And take a look at web site Samsung Galaxy S2 GPS Problem? SOLVED! which talks about how a battery saving option (disabling repetitive polling of GPS data) causes fix issues and how it can be tweaked using another app, GPS control for SGS2 which is mentioned there.

Before starting with these two, just for ruling out false alarms, can you try getting a fix with your Internet connectivity on and in open place where you can see sky like in fields? 

All said and done, I still do not know why magnetic north is flipped in your case!