Two questions:
1) Does anyone know if I can add new image classes to the pre-trained Inception-v3 model? For example, I wanted to train TensorFlow on a multitude of
Yes you can, i recently did something very similar, in my case it was patogenic plant leaves vs healthy plant leaves. The v3 inception is already trained, what you will be doing is transfer learning. Transfer learning is a technique that shortcuts a lot of this work by taking a fully-trained model for a set of categories like ImageNet, and retrains from the existing weights for new classes.
Link : Image Retraining at tensorflow.org
Video Sources: YouTube video tutorial, Hvass Laboratories has some great video resource to rectify your questions.