How do I get my GPS working in Android 4.1 Jelly Bean? Recently I've been having all sorts of troubles with audio and GPS and the compass... I tried different ROMs, different kernels, different patches.

The short story is that after a long time spent messing around trying to get all features working at the same time, in the end I had to factory reset my phone and start anew.

Now, the current situation is that I have a rooted phone running Jelly Bean 4.1. It's freshly installed as of about an hour before writing this.

However, the GPS is unresponsive. Of course I want to fix this, but I don't want to go through the whole mess I just went through over the last few days.

So... how do I get my 
GPS working without playing feature whack-a-mole? I'm taking a breath, slowing down, and I'm looking for a reliable patch or process that I can execute with reasonable assurance and no guesswork.

Specifics are that I have a Samsung Galaxy S2, GT-I9100, issued in Japan. Android version 4.1.2, Kernel 3.0.15-CM (Siyah 5.0.1), Cyanogenmod 10-20121120-NIGHTLY.

Update: The compass issue I mentioned earlier was fixed when I used the build of Cyanogenmod available in this thread on the XDA forum. So I'm now just focused on fixing the GPS.
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!