Is the Mayor aware of the fact that she is the Evil Queen in Once Upon a Time?

To the question title, yes. Regina retains all her memories.

To the question in the body, no, her memories aren't hazy. Regina is the one who cast the curse; from her point of view, she should be the only one who knows their true identity.

Due to Mr. Gold's actions in previous episodes, Regina had become suspicious that he might actually know who he really is. She had to word it carefully so that, if Mr. Gold didn't know he was Rumplestiltskin, he wouldn't think Regina was going crazy. But if he did know, he would answer as such, confirming her suspicions that he did remember.