I wonder if it is possible to write a script that will then "command" Inkscape to draw specific shapes and/or lines of given dimensions and positions.

Not really. I think some work on making Inkscape scriptable was done some time ago, but it was never finished.

The nearest you can get is to write an extension. But then the script has to generate all the SVG code itself, and it can't make use of Inkscape functions such as union, intersection, object-to-path, etc.