I am traveling AA in First Class on a mileage based ticket. Will I be allowed access to the Admirals Club at Newark?

I don't believe first class domestic qualifies you to get into the lounge

I believe by virtue of a first-class ticket it gives you a day pass automatically. Also, if you are active duty military you will be free as well.

You either need to be a member or travelling internationally in First class. Otherwise you won't be. You can also access the club if you have the Citicard AAdvantageExecutive World Elite card. You can also purchase single day passes to the club as well.

Likely only if you are traveling internationally or a member of the club otherwise.