Which postulation ? That C is constant ? There is no postulation of that when you are measuring it.
YES ! Why do you say NO ! You can split experiment into micro sub experiment. It's useless and complicate the setup, but why not ?
There is the synchroniztion problem.
All measure on all sorts of thing are average. When to try to get more and more precision, you start to encounter randomness and start a new physics for those scales (QM).
Yes you can
calculate the speed of a soccer ball, or use GR to have more accurate numbers.
You read wrong - I said you can with a ball...
But I've been hit enough by them to know
that don't match experiment 
Seriously, if its rotating, the speed and steadiness of the win, the humidity, how the ball is made, are all important factor. All chaotic and unpredictable, at normal scale.
All calculus is approximation of situation. Light is in no way different.
All setup spoke about speed of light "in vacuum" for example. You don't put you mirrors in water inside a centrifuge either (the so called inertial FoR)
Why having no mass is important ? Light is there, and then there. Just measure that. It will also work very well for light from space, there are Gillionz of light source out there (but apparently not enough
