And when did length become a basic physical dimension? Does it equate to distance?
Yes, it's synonymous. Your length equals the distance between your head and your toes, even in Mr. Shu's model. More generally, he is talking about the (x, y, z) coordinates in the three-dimensional space of traditional Newtonian physics. But he can't use the plain-English word "space" here because it can be ambiguous and confusing in the context of relativistic physics. Physicists have always
considered this a physical dimension.
The reason Mr. Shu needs mathematical trickery around basic concepts such as length, time, and mass is that he postulates a variable light speed and a variable gravitational constant. This is a problem because an astronomer would measure length in light years, not meters. So how does he distinguish the statements "light speed has gotten faster" from "everything has gotten longer" or "time is running slower"? Similarly, how does he distinguish the statement "the gravitational constant has increased" from "everything has gained mass"? To solve this problem, he needs to do some mathematical legwork to keep his houskeeping consistent. There's no deep insight behind it, just housekeeping.