I would say no. Acting out implies the person who is acting out can't control themselves as if they are a child. It has a negative connotation. Behave or behavior is more neutral and just describes how someone normally acts each day. To behave usually means you behave well. You're a good person who is in control of themselves if you behave or behave well.

Not really. Behave mean to act in a certain way. It could be positive or negative. While act out means to behave badly or in negative way.