How does the Angle of attack vary from the root to the tip of a propeller for a fixed pitch prop?
You are absolutely correct. The "relative wind" at any point on the propeller is a combination of the aircraft's forward motion plus the angular rotation speed of the prop, which is greater at the tips.  This is why, to get the best Angle of Attack, the prop (airfoil) is designed with a twist or "washout" towards the tip.

Notice, with variable pitch props, as the planes forward speed increases, the entire prop AOA
is turned forward to account for change in relative wind.

Fixed pitch props try to find a happy medium between low speed performance and cruise efficiency.  For example, a 10 x 6 (finer pitch) gives better acceleration for take-off, but a 10 x 7 pitch uses less fuel at cruise.