how to solder a 12v regulator?

Try the junk yards that are close to you as a start.

And I love the Desert Fox name brand. Pretty sure they named it after my favorite general!

mmmmm, unless you have an extremely hot air source, let's say something like a jet engine, the answer is no.

If they have about the same Open circuit voltage then you could get some benefit by connecting them in parallel. Just use a charge controller if you value your battery life. A maximum power point controller would give you additional efficiency and protect the batteries from overcharge.

In soldering you melt only the soldering material (not the pieces you want to join) and when it solidifies it holds the 2 parts together (adhesion to each on of them). In welding you melt (at the joint !) all 3 partisipants: The 2 metals and the welding rod..... a "pool" of molten metal is created ...

I would not use this iron on a small circuit board, the temperature control (voltage controller) might help in decreasing the temperature to more appropriate levels 700-800 F if working with lead free solder or 600-700F if done with standard lead solder. Nevertheless, if you do, do it fast, very ...