The 'Rule of Thirds' is neither.
What it is, is a useful referent, so bear that in mind. You use it, not 'follow' it. Think of those points where the lines meet as good places for your subject or eye to rest, but they're also places to move around.... See the frame in that way, and things move around those junctures.
(Also, those thirds lines are *always* a decent place to park a horizon, you may find it edifying to beat that in mind while choosing a composition of something scenic: one thing I don't profess to teach is landscape photo, but if you do that and pay attention to your own reactions you might learn something.
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As for various AF points, these are really a separate matter: the short answer is, it'll be a little more precise if you can put one on the subject. The center point of focus is a range, which if you move the camera makes an arc: the lens' field will be flatter than that arc, so at times using one of the other sensors will be more accurate than focus-and-recompose. But don't arrange your life around it, let's say.