Batteries voltage going down

What you noticed is exactly how solar panels behave when disconnected and then connected to a battery bank.  They have a higher voltage when they're not connected to any load (e.g. a battery bank).  This voltage is called the open circuit voltage of the solar panel (Voc).  You can see the open circuit voltage for the KC130 in its specification page here:

http://store.altenergystore.com/Solar-Electric-Panels/100-to-149-Watts-Solar-Panels/Kyocera-Solar-KC130TM-130W-12V-Solar-Panel-w-J-Box/p2403/

Once they are connected to the battery bank they are forced to operate at the same voltage as the battery bank (which in 12V system could be anywhere from about 10 to 14V DC).

If your concerned that your solar panels are working at lower voltage than their maximum voltage and that you might not be getting all of the power that you could otherwise get - you're not too far off from being right. The catch is that the solar panels don't produce their maximum power at their highest voltage (which is the voltage you see when the panels aren't connected to anything).

Every solar panel has a defined voltage where it optimally operates and produces the most power (Power = Voltage x Amperes). This voltage is called the maximum power point voltage (Vmp). You'll see in the spec page for the KC130 the max. power voltage is 17.6V DC. So yes, when your solar panels are connected through the Flexcharge charge controller and then the battery bank they are forced to operate at a voltage below the maximum power voltage (they forced to operate at the battery bank's voltage).

The problem isn't your solar panels and in reality that's how the Flexcharge charge controllers work.  They aren't sophisticated enough to allow the panels to operate at their optimal voltage and at the same time allow the batteries to work at their lower voltage.   In fact, this is the way all charge controllers used to work until the advent of Maximum Power Point Tracking (MPPT) charge controllers. Only MPPT type of charge controllers can efficiently convert a solar panel's higher optimal power voltage down to a battery bank's voltage.

For examples of MPPT charge controllers see:
http://store.altenergystore.com/Charge-Controllers/Solar-Charge-Controllers/MPPT-Solar-Charge-Controllers/c474/

Using what I refer to as "traditional" charge controllers means that when a battery bank is really low (and has a really low voltage) the solar panel is made to function at a  voltage that's really far from it's optimal power producing voltage (e.g. it may be forced to work at 10.5V instead of 17.9V).  As a result, the solar panel will actually produce 30% less power than it would if it was at its optimal voltage (that's a lot of power loss!).

Same case as with Jorge above. Everything is working exactly as it should. Because you're not using a charge controller with MPPT technology then your PV is forced to operate at the same voltage as your batteries. The highest your PV voltage will rise to will be the full voltage of your batteries, which is around 14 plus volts.

Running your diesel engine to charge up the battery bank would not damage your PV nor your charge controller. It would just make your batteries full and happy really fast.

Also, remember that a battery bank's voltage changes when you hook a load up to it. At rest, the battery bank full charged may be say 14.4V.  But the moment you run a load on that battery bank (e.g. a bilge pump, lights, radio, etc) that voltage will dip a bit ... like down to 13.3V. As soon as you remove that load you'll see the voltage will actually creep up again. If you only ran the load for a very short period of time, the voltage may rise right back to the full voltage (14.4V). That's all ok and normal.