You have two options, return the battery to 6V or make the decision to change to 12V and replace generator, coil, lights and regulator. Your starter is not as important. A 6V starter will operate on a 12V system without any issue however you MUST not engage it for long! A 6V starter on a 12V system will burn out quickly if engaged for too long. If you machine doesn't start quickly then let the starter cool before trying again.
14 gauge should be fine. That's what mine has. Clean weatherproof connections are important.
Comment on the black spark plugs, I wouldn't worry about them until you've sorted your other issues out. Chances are what is happening is that your spark is getting weak (from the voltage issue) then finally dying and by this time your plugs look a mess.
Once you have a 12V coil your points should be fine as long as they are not burnt out already. It is the combination of 12V battery and 6V coil that is brutal to the points!