What is the proper way to bin variables for calculating WoE during credit scoring?
Or is there any algorithm/function that bins continuous variables in most practical way.

Sure there is, but that's the wrong question: the standard method for discretizing a continuous variable consists in splitting the values into equal intervals, that's it. Of course it doesn't guarantee any of the 5 conditions, since these conditions are about additional constraints almost exclusively related to expert knowledge and the specifics of the data.
Note that these conditions can certainly be automated, there's no need for manual verification. There might be some domain-specific packages which do this for you, but there's no reason a standard ML/statistics library would provide methods for every specific problem like this one.