Anx yes, panic no. Atarax (hydroxyzine) is an antihistamine, and like others in this category, has a calming and sedating effect, usually mild in the usual doses given. Thus, it is a safe and non-addictive option to treat anxiety. Panic attacks are a different thing: sudden, intense, often not triggered by anything obvious. Atarax probably won't help with panic.
Maybe a little. Atarax (hydroxyzine) is an antihistamine, which can have some calming effect. Although it's not clear it would stop a full-blown panic attack, it might help at least for awhile with anxiety. However, if you are having anxiety and panic attacks, you would be best served by seeking out a psychiatrist (or child and adolescent psychiatrist if this is for a child) knowledgeable about treating this.