For curves, all this paragraph is saying is to simplify curves into a chain of straight lines because by doing so we end up with some clearer landmarks which we can then position at specific points along the length of a given dimension. By doing this we remove the curving aspect out of the object completely simply because curves are imprecise and that goes against what the lesson is about.

For the mouse, uncomfortable's demo actually ends up quite imprecise which means that the land marks he drew on the orthographic plans aren't actually transferable to the object construction which means that you're essentially guessing where things are meant to be placed. This draw over of his plan, uses subdivision more effectively to place certain landmarks which can be transferred over to the 3D construction. So if you make orthographic plans before drawing each object construction it essentially is simplified down to copying the plan onto the construction.

For the rest of your concerns, you seem to be confused at how things are placed. The general process of this lesson goes like this, you first pick an object to construct. You then observe the object closely and make orthographic plans for different views of the object, after making the orthographic plans you then construct a bounding box for the object and transfer the plans to the object. The hardest part of this lesson is transferring the plans to the object and your brain will feel like its going to explode while trying to do so. So the thing you will spend most of the lesson doing is observing the object and making the orthographic plans.

Orthographic plans are critical because they separate the decision making process from the 3D construction process because by making decisions of where everything will go before drawing the construction you can focus fully when you are drawing the construction. Note that I said "make decisions" - this is not about finding the "correct" proportion, but rather deciding which one you will be using. So if you had a drawer face with a handle on it, and that handle extended from the 19/50ths subdivision to the 31/50ths subdivision, that's... a lot to ask of a person. There's not a lot lost in rounding it to 2/5ths and 3/5ths, as long as that rounding doesn't accidentally eliminate some other important elements as a result. If you want examples of precise orthographic plans you can take a look at my submission.

Hope that answers your questions!