How frustrating. It sounds like you have an inflexible person working in a program that should be flexible. Remember to document all of your conversations with this person -- sending an email confirming your understanding of what she said can be a non-threatening way to do this. You may have to go to her supervisor if the situation becomes untenable.
Artwork -- maybe you could give a little ground and concede that she can have some of the art work but ask if she will accept pictures of the artwork that you really love and want to keep. If proof is what she wants then pictures should suffice. I can't imagine that she really wants to keep a bunch this stuff, especially if it is 3D.
Oral responses -- I can understand her desire for some written work. I would ask if periodically you could record or scribe (type your son's oral responses) your in-depth oral discussions. There are many gifted kids this age who can't produce writing commensurate with their oral abilities. Also, if your kid is on an IEP for speech, maybe you could include oral responses as a goal so that you are fulfilling an IEP goal while meeting his gifted needs.
PE -- I agree with others that there should be some room for compromise here. Find out what her documentation requirements are and find our what your instructors are willing to do.
