Indeed. But keyword is „inferred“, assuming that all laws worked the same at any point in a gigantic timeframe, at any point in a gigantic universe. Except singularities. And quantum mechanics as it seems? And maybe dark energy. Oh and lately, maybe gravity waves. Btw I was once in a lecture room in Berlin where they claimed that one of the thermodynamic laws where discovered…while giving a lecture. Not too long ago, perhaps 150-200 years. Doesn‘t seem so unlikely that somebody comes up with a new version at some point.

No, not literally…presumably. You believe that the radiation you look at is that old, because you measure certain wavelengths and study ladders, but you can‘t really prove it. Proving that something is 13 billion years old is beyond the capabilities of us apes, at least at this point.