1: Previous conditions in fluids cannot be determined with any kind of accuracy except for really obvious cases like "did this wet ground come from a cloud?" or laminar flows (https://www.youtube.com/watch?v=p08_KlTKP50). Since weather is fluid mixing at high speeds with low viscosity, there is a huge amount of turbulence and entropy. Entropy means systems are not time-reversible.

2: Can we predict weather 2000 or 1M years ago based on estimates of temperature and geography? Yes, pretty reliably. Vegetation and albedo are some of the biggest variables- plant transpiration puts huge amounts of water into the air and changes surface temperatures. But we have a pretty good idea of the geography, and relatively small changes don't have a huge impact on general weather trends.

3: Can we predict the exact weather on a day 100 years ago, given available measurements? No, not really. Without satellites you need radar, and without radar you need weather balloons. Coal burning also had impacts on weather. Low pressures at the surface can tell you that the weather may get worse, but it doesn't tell you where its coming from or what the higher airflows are doing.

Does anyone have a nice website for looking at past weather? I often could use it.