We are decades away from asteroid mining at best, even assuming we go all in starting today. The difficulties and numerous engineering challenges of mining at zero g cannot be understated.
No. A gear train is just a transfer of force/torque. It's analogous to a simple lever for rotational motion. Mechanical impedance is almost always referring to harmonic forces (think of spring systems and structural dynamics). Impedance in fluids also fall under mechanical impedance but it's usually classified separately as acoustic impedance.
The whole article appears use a very loose philosophical definition of "impedance". As a mechanical engineer, none of the mechanical examples are correct either when there are real-world examples that actually meet the more strict technical definition of impedance matching, mass-damper systems in skyscrapers is immediate example that comes to mind.
They started developing this rocket in the late 2010s, way before the current US craziness (or the current level of craziness anyway). Independent access to space is always desirable for countries that can muster the resources, but this is just one of many companies that appeared back then as a response to SpaceX's initial success.