Yesterday on a one Polish FB group for fans of history someone asked about the date of Jesus' birth. One person has jumped out with some picture of a wildly specific dates for many Biblical events regarding Jesus. ( here is the pic https://imgur.com/a/hB6VYwK ). The other guy came in and started to criticize saying that history doesn't have any good proof for almost anything about Jesus story except some basic facts like that he existed. So the dates from the picture are some theological rubbish, not a historical research. The first guy defended it saying that this is exactly what historians do, speculating like that based on available sources and it is a legit, research valid chronology. Someone else has linked to another very oddly specific chronology: http://nowoezone.com/NTC09.htm?fbclid=IwAR2CfrimmgjLheUxyvQuZqS9IIwdpx2C0gyGqnh3I7mlMGRAPFTk_-3Yat4

So here is my question or rather few questions. I am not a historian and have no idea how you guys do your job. I am bit baffled by what those people were saying. So:

1. Do those chronologies which I linked above have any scientific academic merits or if you would try to push forward something like this in a historical (not bible studies/theology) department you would be laugh off?
2. Do we really have enough sources to do any such specific dating like this? I know that the consensus is Jesus existed and probably died on a cross and was baptized. So the sources are rather vague if that the really best of the consensus historians reached. Or am I wrong?
3. If the sources are really vague and the research shown above is academically valid then: Do we really should trust any research regarding ancient/medieval times? I am not meaning healthy dose of everyday skepticism but the fact that we (laymen) treat most of ancient history told to us in school and everywhere as facts. And if a research is based on a really obscure vague sources then it is more in realm of wild speculations if it gives so much specific information.