lol, you want something to touch? Man, you make absolutely no sense. There is no such thing as infinite degree of precision and it's not practical. And the constants generated are a byproduct of the chosen method/model of analysis, ambient conditions, and the analysis itself. Physics constants do exist if you believe order exists and that things can be related. If you don't think that, then you either think order doesn't exist or that things can't be related. In that case, everything is just 'magic', just coincidence.
You really have no room to be talking about what modern physics can and can't do if you don't even know what modern physics does. You're just stating a position from a significant level of ignorance. It's like those politicians attempting to take a scientific side when they have no idea of the science. Their stances are just as silly as yours. They don't go for absolute accuracy, they build models to compensate for varying factors to within acceptable and practical purposes. The whole Mars rover thing just happened to work out by magic? The way they build electrical systems and all those technological feats, all just magic? No modern physics involved huh?
General disclaimer: I don't know if I'm right on most of this cause I've only had limited exposure. Better off asking this in physicsforums.com.
Yes, even if the observer is traveling at 50%, light still travels at the same speed relative to that observer. And the thing about the gravity well is gonna take some explaining, why I said free space in the original thing. You won't have the same kind of observation if you subject the light to a gravity well. There's a thing called gravitational lensing. This has to do with the dual nature of light, how it behaves like a particle and wave (think Einstein won his Nobel Prize for this specifically, predicting gravitational lensing). Light bends when it passes by things with gravitational significance. So you won't have the same judgement of measurement. The best way I can explain is with a sort of simplified example to illustrate.
You end up observing bent light which throws off the calculation of speed of light because of the distortion since light behaves like a particle, which are subject to gravitational fields.
I don't know if that makes sense. You don't get an accurate measurement of the true distance traveled so can't get the true measurement of the speed of light because of your distorted observation. However, I think there are ways to compensate for it, but this is kinda beyond my ability. I'd have to take a hard astronomy course.