The distribution of dataset train and test are the differents, how to fix this?
how does it compare to longer timespans? Can you still observe noticeable drift?
to some extent this is usual behaviour
here is a guide for KL divergence, It's just a tool you can use to compare probability distributions.
exploration is equally important as hard stats. For me those plots look alright. There's no defined point, telling you when you can or cannot do things. That's whole point of ML, you don't have a priori knowledge. Best run some models and check validation metrics.