I agree with that. No matter what you try to communicate through art, someone else will see it differently, and no matter how true you felt the meaning or purpose you put into the piece was, the meaning that someone else takes from it will be just as true and important. It will just be their version of the truth in the piece. Once it's been seen by other people, its meaning becomes subjective, and there's nothing anyone can do about it. Even if you find a way to explain in the work itself what its purpose is, someone will take that, possibly, as a comment on the prevalence of the perception that all art has a inherent meaning.
You can imbue artwork with symbolism, which would go towards achieving what you spoke of, but it will still be quite subjective. A symbolic painting I saw recently depicted a girl sitting at a train station as symbolic of the uncertainty of hope: she was waiting for the train, but it hadn't come yet and she'd been waiting a while (there were things in the painting to indicate this). I took it to be a comment on youth-- starting out on life's journey-- and the optimism that often accompanies that. Art is tricky, but that's why I like it so much.
On your first question, I sue hope INTP's can be good artists. Otherwise I'm going to be a very hungry animator.