Alternator is dying. VW content

So here I am, hanging onto a modernist VW for far longer than any sane human should.  I bought it in 2012 and have put nearly 100,000 miles on it (at 155,000 now).  For those who don't remember it's an 07 Passat wagon VR6 4Motion.  
 

So the past couple of days I've noticed it's been notably sluggish to start.  Stop at my local auto parts store and the dude says that it's putting out the correct voltage but is only 31% charged.  I start the car and running voltage at the battery is.......12.9 

Recheck when I get home And the OBD scanner agrees, 12.9-13.0 volts.  She's running but I certainly don't want to count on it for long.

So far this has just been me whining so here are the questions to the hive:  1=It appears like I have to unbolt the AC compressor and let it swing out of the way to access the alternator from below, is this correct?  Fairly rare car has very few "how to" videos on YouTube.

2= when I went outside to move the car into the garage I noticed the fuel pump is just running (no key in car).  Got it in the garage and it was more notable and only stopped when I disconnected the battery. Is this related to funky voltage in the system, VWs hate low voltage and will do weird stuff when the alternator dies (actually had it replaced under warranty about 3 weeks after I bought the car).   
 

Thanks in advance for any help gang.

A dying battery can pull the system voltage down quite a bit. Try hooking up a secondary battery and see if it jumps up to proper voltage. If not, alternator. 

Probably worth checking parasitic losses as well.

As far as changing it... you will have to move the compressor without disconnecting it from what I remember. 

Any ideas about the fuel pump staying on?

I agree a dying battery can often have same symptoms as a bad alternator. Had a battery less then a year old go bad. Had auto parts store do a load test and battery tested ok. Did out put on alternator and it was ok. Went right back with another load test on battery and it showed weak. Changed battery under warranty and never had another problem.

Replace the alternator and or battery, then worry about the fuel pump.  Low voltage can cause strange things to happen.

The 3.6 fuel pump is ecu PWM controlled from what I remember. If voltage is off, I wouldn't trust a thing it does.

Update:  turned out to be a bad/failing fuel pump controller.  Once again I should have taken it to the shop first and let them diagnose it.  Ah well, I have a new alternator and battery at least.