Theory: Gradient with respect to particle i

Hey guys

I've been trying to understand a thing which is explained a bit in this answer:

I understand everything up to:

1) I don't understand how he goes from nabla W to W' and an r hat vector.

2) Also I don't understand what is the difference between nabla and ' in this case. I understand nabla is spatial derivative with respect to xyz, while ' might be with respect to q = r/h ?

3) What does the hat vector really mean? Is it just that:

r = (x,y,z) ----> r_hat = (-z,y,x)

But as far as I know a lot of different r_hat can exist in 3d?

I hope someone would take a bit of time explaining this concept to me or maybe guide me to another explenation of how to understand gradient with respect to i computionally.

Kind regards
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