1. What is your age?
16

2. What is the highest level of education you have completed? i.e. some high school, high school, some college, college, grad school, etc.
Some High School.

3. Referring to English, do you know what a double negative is?
Of course.

4. Do you feel it is acceptable to use double negatives in everyday speech.
It depends; i.e., if you're discussing decisions, someone could say "I can't not do anything", which I find to be acceptable. But otherwise, no.

5. Do you feel it is acceptable to use double negatives in college and high school level papers?
No, but the same rule applies here.

6. Do you consider the following sentence to be acceptable: John doesn't
know nothing.
No, I don't. Although it does make sense, it's grammatically incorrect.