For experienced lifters, the program is set up to be modular and instinctive. There's no one "right" way to do it, no matter how closely you fit any particular profile. And the profiles I made up aren't meant to be definitive -- they're just examples of how the programs could be done, not how they should be done.
In general, Fat Loss I and II are beginner-level programs, and are meant to follow directly from the Break-In Program. Hypertrophy I and II are advanced beginner/intermediate-level programs. The Strength programs are meant for more advanced lifters. Fat Loss III and Hypertrophy III sort of straddle the zone between intermediate and advanced.
How you arrange them is really up to you. The only "rule" I'd suggest is to avoid jumping around from beginner to advanced to intermediate programs. I'd try to do them in a linear way, from beginner to intermediate to advanced.
So I wouldn't go from Hypertrophy I to Fat Loss III. But it's fine to go straight from Fat Loss II to Hypertrophy II, if you want, or from Hypertrophy II to Strength I. Even though you're jumping tracks, you're landing on tracks that are heading the same direction.
It's fine to modify your form on the front squat, and it's fine to do four workouts a week instead of three, if that what your instincts tell you to do.
The key is to make the book work for you, and there's no single way to do that.
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