1. What is your age? 45
2. What is the highest level of education you have completed? Grad school (M.A.) and professional school (J.D.) so far
3. Referring to English, do you know what a double negative is?
Yes. (Here it was difficult not to write "not hardly.")
4. Do you feel it is acceptable to use double negatives in everyday speech.
Depends on whether or not you're attempting to use standard speech or colloquial. I personally don't use them unless I'm quoting someone or just wanting to sound like a hick.
5. Do you feel it is acceptable to use double negatives in college and high school level papers?
Not if you're wanting to get an A, generally, or not be marked down for non-standard use of English, which teachers are often grading for. But again, it might depend. Such a construction might be perfectly acceptable if it were used in dialogue on a creative writing project or part of a quote included in the paper.
6. Do you consider the following sentence to be acceptable: John doesn't know nothing.
I consider it both acceptable and understandable, even if it's not considered "standard English." But I'm not a high school English teacher any more. Teachers are funny about stuff like that. I happen to like colloquial expressions and variety in speech.