The laws may not have changed, but our understanding of them certainly has...and continues to, as well.
I'm not quite sure what you're getting at here, yes our understanding of the laws of nature continues to improve and therefore makes our understanding of the past more accurate
In some cases. What evidence is left behind when an organism dies and then biodegrades (assuming that it is not fossilized)?
One of the key things people look at in Archean and Hadean are Carbon 12 "smudges" that have been fossilized (ie it is not the same as Carbon dating, as this only works to ~50,000 years ago). Combining this with also looking at at other key elements in rocks (Nitrogen, Phosphorous, Oxygen etc) can tell us how life was manipulating the conditions at the time.
They recreated that conditions that existed when the earth was "young" in a lab? Cool story. How do they know what the conditions were?
Simple answer, rocks. The Archean in particular is known for its high volume of igneous rocks, combining this with the knowledge that the Earth's interior was much hotter than present means that there must have been significant volcanic activity at the this time, on a scale many times current activity. This scale of volcanics has huge consequences for the atmosphere, particular sulphur dioxide, ammonia and carbon dioxide.
We also know that there was liquid water at this time, due to the presence of gneisses which require liquid water to form. We also know there was a lot of carbon dioxide in the atmosphere because there are almost no carbonate rocks from this time because the sea was acidic due to dissolved carbon dioxide.
I read some of it, a lot of it was speculation being expressed as assertions.