grammar - Use of 'not' in questions

When is it okay to use 'not' when posing a question?
I believe that the person asking would include the 'not 'when he believes the implied to be true.
For example:
"Are you going to the store?
"Are you not going to the store?"

Then the question of how to properly answer it.

"Yes, I am going to the store"
"No, I am going to the store."

and if they arent going...
"No, I am not."
"Yes, I am not."

I wonder if this is a French rule and therefore confusing to English speakers; where 'Si' is used instead of 'Oui'.

Anyways, your thoughts?