I was born in Germany.my dad was in the air force.my mom is American.i have a German birth certificate and a us birth certificate.?can I move to Germany to live.??

Since non of your parents have the German Citizinship you can’t. The German Birth Certificate does not grant you citizenship.

If you mean German Air Force yes. If not potentially you might be able to.

Theres a nice function that called visa navigator. Yes you can move to germany and can apply there for a work visa.

I was born in Germany by a German mother and American father, am I intitled to German citizenship