No it isn't. If it was, a NIST optical clock at the floor would run at the same rate as a similar clock up at the ceiling, and my pencil wouldn't fall down.... So, yes your room is infinitely small compared to astronomical dimensions.
No you wouldn't. Those optical clocks run at different rates because they're in a place where the speed of light is spatially variable. Curved spacetime is where this variation is not linear, where there's a tidal force and g varies. Rpenner will verify this.And if you measured the speed of light over a finite distance, you would naturally take curved spacetime into consideration.
Rpenner: please change this thread title to Einstein's GR versus cargo-cult GR.