If I recall correctly, Giovanni kneads his dough by hand. So he will always have better "control" over the dough than you will get with a stand mixer. With a stand mixer, and especially with a small amount of dough, you will frequently have to stop the machine to make adjustments: to get the dough ball off of the hook, to reorient the dough so that it kneads better, to scrape the sides of the bowl to get splattered flour or dough back into the game, to shape the dough into a ball because the machine isn't doing it well, etc. And there's nothing wrong with having a spoon or spatula on hand to help. One thing you might try in future efforts is to start with the paddle and then switch over to the hook when the dough looks like it is coming together. You might also start with some of the flour and a little of the water so that you don't immediately get a sticky mess. There's no real right or wrong way. Some recipes say to throw everything into the bowl at the same time (Peter Reinhart does this with his dough recipes), others say to start with the water (the Tom Lehmann approach) and then add the dry ingredients (all at once or in stages), and still others say to start with the dry ingredients and then add the water. With experience, you will figure out what works best for you and your particular machine.
As for your dough, you should have oiled the entire ball before putting it into the freezer/refrigerator to prevent the outer surface from drying out and forming a crust. If a crust does form, you can soften it a bit by rubbing a little bit of water or oil over the dried out area. Then cover the dough with plastic wrap or a towel to keep it soft until you are ready to work with it. If you find that the dough is still sticky when you are ready to work with it, you can add a little bit of flour on the work surface, as previously mentioned in an earlier post. But don't punch down and re-ball the dough. This will result in reorienting the gluten strands and make the dough overly elastic and hard to shape without experiencing snapback. It will also expel the gasses trapped in the dough.