There are some models pretrained on imagenet which generalise very well even for unseen classes.
You can trust that if you have no much clue about what u are doing.
If the model is not trained then yes, you should train it in your dataset.
Anyway randomly-initlised CNNs still works better than random.
The pth file is a compressed file, it contains what you save into it.
Assuming you saved the weights of your model, then yes.
You can do both, use the model on-the-fly if you have a good GPU and a small hard disk or save the tensor if you need it.
That’s up to your necessities.
Models usually have a last layer to compute class probabilities. If you train your model from scratch you can just delete it. If you use a pretrained model you need to keep it as you will have an error otherwise.