How to train on extended data set correctly

I have trained my classifier on pictures with a mixture of several classes
on each picture, e.g. A-F. The classifier is able to (nearly) correctly segment those classes
on the images.

Now I got more data with pictures showing class G. To minimize my work, I only labeled
class G on the images and left the rest out (Invalid).

Two questions for my training arise:

1. If there are no examples of class G in my first dataset (because it could have been a subclass
   of A-F), how do I train it correctly?
   Suggested Solution: I can add my new data to the old one, but I have to tell the CNN when there is an image with class G, because I have to change the error measurement of my CNN somehow. But how?
2. If G was included in my first dataset (assume G is ‘police car’ and B is ‘car’, but
   some images showed police car), how do I train in this case correctly?