Wrong.
The moment you have chosen the pressure angle and the diameter of your hob, you have set all choosable parameters. The pitch of the hob - if you choose to make a hob with pitch - is then the width of (a multiple of) one tooth at the pitch circle diameter - a derived quantity.
Wrong again. Geometrically speaking, the transformation you need to do to get root clearance is called shearing, not rotating. The difference between the two is that in shearing, top and bottom surfaces of your tool remain horizontal; with rotating, they do not. Thus, if you view the tool in your shadowgraph, the cutting surface on which you focus has to be horizontal as well. Rotating the cutter, as your picture shows, is a crutch that can work, but, as your question shows, leads to misunderstanding of what happens during the hobbing process. By recommending this rotation, your book is leading you astray.
Should you decide to make the cutter / hob without pitch, you need to build your tooling such that both hob and gear rotate in concert. A hob with pitch can be operated by and large without that constraint.
To understand what I have said here, visualize the hob as a (rotating) broach. If there is no feed forward of the broach during gear cutting (i.e. the hob has no pitch), the gear shape is a direct copy of the cutter shape and not an involute curve. Thus, your milling machine needs to supply that feed forward, and it also needs to couple that to the rotation of the gear blank. But if you build your broach in the form of a screw, feed forward is part of the broach (a hob is another name for a rotating broach), and if you permit your gear blank to rotate freely, the hob will do the move forward action for you - just make sure to pre-cut the blank enough that the hob does not slip.

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