Questions about Free Will Theorem

[exponent137]

http://arxiv.org/abs/quant-ph/0604079
The TWIN axiom:. For twinned spin 1 particles, if the first experimenter
A performs a triple experiment for the frame (x, y, z), producing the result
x → j, y → k, z → l while the second experimenter B measures a single
spin in direction w, then if w is one of x, y, z, its result is that w → j, k, or l,
respectively.
1. Why the second experimenter performs only single spin measurement. If the first one performs three measurements, the second one could also perform three.?
2. I here included measurements of the second one in the direction, for instance, 45° acording to x and y axes.

Lemma: There is no 101-function for the ±33 directions of Figure 1.
How 33 directions in cube picture in the article are connected with those measurements of spin^2?

 

[exponent137]

Now, I went through http://www.ams.org/notices/200902/rtx090200226p.pdf
and I partially followed the ideas. In principle they rotate only one xyz axis for 45° in some directions and they controll if functions 101 agree with pre-existence of different rotations. I need to study more precisely.

This is improvement of Bell's theorem. Does Free-Will-Theorem tells anything about that free will decision about directions of measurement is connected with free will of a wave function how it will collapse?