Get another standard rod that is as long as needed, or (more commonly) get a large number of very small standard rods and count how many are used.
That is all we are saying. Those caveats are acceptable. The geometry we are interested in spacetime is the spacetime interval.
Not really. The origin can be moved in time as desired without even changing the components of the metric tensor. And you can do a diffeomorphism to a coordinate system with any arbitrary origin. Such a transformation will cause the components of the metric to change, but all measurements of spacetime intervals will be unchanged. Since such quantities do not depend on the choice of coordinate system you can express them without reference to any coordinate system if you wish. That is the point of coordinate-free relativity.