Understanding Sarsa's linear, gradient descent (based on Sutton & Barto)

Question

I am trying to implement Sarsa linear gradient descent based on the Sutton and Barto Book , see the algorithm in the figure below.

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However, I am trying to understand something in the algorithm:

Is the dimension w and z independent of how many different actions can be taken? It seems that in the book they have a dimension equal to the number of functions that, I would say, are independent of the number of actions.
Are there w and az for each action? In addition, I do not see in the book that this should be so.
If I am right in the two above brands, then I don’t see how the F_a index will depend on actions, and therefore I don’t see how the q_a action function can affect actions (see lines marked with yellow in the algorithm below). But action-value should depend on action. So I'm not getting something ...

I hope someone can help clarify this for me :)